Corresponding characteristics of graphs of ƒ and ƒ' - AP Calculus AB
Card 0 of 55
A jogger leaves City 
at 
. His subsequent position, in feet, is given by the function:
,
where 
is the time in minutes.
Find the acceleration of the jogger at 
minutes.
A jogger leaves City
where
Find the acceleration of the jogger at
The accelaration is given by the second derivative of the position function:
For the given position function:
,
,
.
Therefore, the acceleration at 
minutes is 
. Again, note the units must be in 
.
The accelaration is given by the second derivative of the position function:
For the given position function:
Therefore, the acceleration at
Compare your answer with the correct one above
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after 
seconds. What's the acceleration in 
of the block after it has been ejected?
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and 
. Acceleration, in this case, is gravity, which makes sense that it should be a constant value!
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and
Compare your answer with the correct one above
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
Notice that the function 
is simply the derivative of 
with respect to time. To see this, simply use the power rule on each of the two terms.
Therefore, 
is the rate at which the car's speed changes, a quantity called acceleration.
Notice that the function
Therefore,
Compare your answer with the correct one above
The function 
is a continuous, twice-differentiable functuon defined for all real numbers.
If the following are true:
Which function could be 
?
The function
If the following are true:
Which function could be
To answer this problem we must first interpret our given conditions:
Implies the function is strictly increasing.
Implies the function is strictly concave down.
We note the only function given which fufills both of these conditions is 
.
To answer this problem we must first interpret our given conditions:
We note the only function given which fufills both of these conditions is
Compare your answer with the correct one above
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after seconds. What's the acceleration in of the block after it has been ejected?
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and . Acceleration, in this case, is gravity, which makes sense that it should be a constant value!
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and
Compare your answer with the correct one above
A jogger leaves City at . His subsequent position, in feet, is given by the function:
,
where is the time in minutes.
Find the acceleration of the jogger at minutes.
A jogger leaves City
where
Find the acceleration of the jogger at
The accelaration is given by the second derivative of the position function:
For the given position function:
,
,
.
Therefore, the acceleration at minutes is . Again, note the units must be in .
The accelaration is given by the second derivative of the position function:
For the given position function:
Therefore, the acceleration at
Compare your answer with the correct one above
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
Notice that the function is simply the derivative of with respect to time. To see this, simply use the power rule on each of the two terms.
Therefore, is the rate at which the car's speed changes, a quantity called acceleration.
Notice that the function
Therefore,
Compare your answer with the correct one above
The function is a continuous, twice-differentiable functuon defined for all real numbers.
If the following are true:
Which function could be ?
The function
If the following are true:
Which function could be
To answer this problem we must first interpret our given conditions:
- Implies the function is strictly increasing.
- Implies the function is strictly concave down.
We note the only function given which fufills both of these conditions is .
To answer this problem we must first interpret our given conditions:
We note the only function given which fufills both of these conditions is
Compare your answer with the correct one above
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after seconds. What's the acceleration in of the block after it has been ejected?
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and . Acceleration, in this case, is gravity, which makes sense that it should be a constant value!
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and
Compare your answer with the correct one above
A jogger leaves City at . His subsequent position, in feet, is given by the function:
,
where is the time in minutes.
Find the acceleration of the jogger at minutes.
A jogger leaves City
where
Find the acceleration of the jogger at
The accelaration is given by the second derivative of the position function:
For the given position function:
,
,
.
Therefore, the acceleration at minutes is . Again, note the units must be in .
The accelaration is given by the second derivative of the position function:
For the given position function:
Therefore, the acceleration at
Compare your answer with the correct one above
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
Notice that the function is simply the derivative of with respect to time. To see this, simply use the power rule on each of the two terms.
Therefore, is the rate at which the car's speed changes, a quantity called acceleration.
Notice that the function
Therefore,
Compare your answer with the correct one above
The function is a continuous, twice-differentiable functuon defined for all real numbers.
If the following are true:
Which function could be ?
The function
If the following are true:
Which function could be
To answer this problem we must first interpret our given conditions:
- Implies the function is strictly increasing.
- Implies the function is strictly concave down.
We note the only function given which fufills both of these conditions is .
To answer this problem we must first interpret our given conditions:
We note the only function given which fufills both of these conditions is
Compare your answer with the correct one above
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after seconds. What's the acceleration in of the block after it has been ejected?
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and . Acceleration, in this case, is gravity, which makes sense that it should be a constant value!
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and
Compare your answer with the correct one above
A jogger leaves City at . His subsequent position, in feet, is given by the function:
,
where is the time in minutes.
Find the acceleration of the jogger at minutes.
A jogger leaves City
where
Find the acceleration of the jogger at
The accelaration is given by the second derivative of the position function:
For the given position function:
,
,
.
Therefore, the acceleration at minutes is . Again, note the units must be in .
The accelaration is given by the second derivative of the position function:
For the given position function:
Therefore, the acceleration at
Compare your answer with the correct one above
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
Notice that the function is simply the derivative of with respect to time. To see this, simply use the power rule on each of the two terms.
Therefore, is the rate at which the car's speed changes, a quantity called acceleration.
Notice that the function
Therefore,
Compare your answer with the correct one above
The function is a continuous, twice-differentiable functuon defined for all real numbers.
If the following are true:
Which function could be ?
The function
If the following are true:
Which function could be
To answer this problem we must first interpret our given conditions:
- Implies the function is strictly increasing.
- Implies the function is strictly concave down.
We note the only function given which fufills both of these conditions is .
To answer this problem we must first interpret our given conditions:
We note the only function given which fufills both of these conditions is
Compare your answer with the correct one above
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after seconds. What's the acceleration in of the block after it has been ejected?
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of $s=220t-16t^2$ after
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and . Acceleration, in this case, is gravity, which makes sense that it should be a constant value!
Since $a=\frac{ds^2$$}{dt^2$}$, by differentiating the position function twice, we see that acceleration is constant and
Compare your answer with the correct one above
A jogger leaves City at . His subsequent position, in feet, is given by the function:
,
where is the time in minutes.
Find the acceleration of the jogger at minutes.
A jogger leaves City
where
Find the acceleration of the jogger at
The accelaration is given by the second derivative of the position function:
For the given position function:
,
,
.
Therefore, the acceleration at minutes is . Again, note the units must be in .
The accelaration is given by the second derivative of the position function:
For the given position function:
Therefore, the acceleration at
Compare your answer with the correct one above
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
Notice that the function is simply the derivative of with respect to time. To see this, simply use the power rule on each of the two terms.
Therefore, is the rate at which the car's speed changes, a quantity called acceleration.
Notice that the function
Therefore,
Compare your answer with the correct one above
The function is a continuous, twice-differentiable functuon defined for all real numbers.
If the following are true:
Which function could be ?
The function
If the following are true:
Which function could be
To answer this problem we must first interpret our given conditions:
- Implies the function is strictly increasing.
- Implies the function is strictly concave down.
We note the only function given which fufills both of these conditions is .
To answer this problem we must first interpret our given conditions:
We note the only function given which fufills both of these conditions is
Compare your answer with the correct one above