# Calculus 1 : How to find slope by graphing functions

## Example Questions

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### Example Question #21 : How To Find Slope By Graphing Functions

Find the slope of the equation  at the point .

Explanation:

The slope of a function at a given point is found by first taking the derivative of the function.

Use the power rule to find this derivative, given by:

By evaluating the derivative when  you will find the slope of the function at the point .

### Example Question #22 : How To Find Slope By Graphing Functions

What is the slope of at ?

Explanation:

To find the value of the slope at , you must first find the derivative of the function since that will give us the slope. To take the derivative of a term, multiplty the exponent by the coefficient in front of the  term, and then subtract  from the exponent. Therefore, the derivative is: . Then, plug in  to get the correct slope value. .

### Example Question #23 : How To Find Slope By Graphing Functions

What is the slope of at

Explanation:

To find the slope, you must first find the derivative. To take the derivative, multiply the exponent by the leading coefficient and then subtract 1 from the exponent. Therefore, the derivative is: . Then, plug in 2 to get the specific value: .

### Example Question #24 : How To Find Slope By Graphing Functions

What is the slope of when

Explanation:

To find the slope, you must first find the derivative function. To take the derivative, multiply the exponent by the leading coefficient and then subtract 1 from the exponent. Therefore, the derivative is: . Then, plug in -1. .

### Example Question #25 : How To Find Slope By Graphing Functions

What is the slope at x=1 if ?

Explanation:

To find the slope, you must first find the derivative of the function. To take the derivative, multiply the exponent by the coefficient in front of the x term and then subtract 1 from the exponent: . Now, plug in 1 for x to get your answer of x=5.

### Example Question #26 : How To Find Slope By Graphing Functions

Find the slope of the line tangent to the curve of g(x) when x is equal to 5.

Explanation:

Find the slope of the line tangent to the curve of g(x) when x is equal to 5.

To find the slope of a tangent line, first find the derivative of the beginning functions:

Will become:

Next, simply plug in 5 everywhere we have an x and solve.

### Example Question #27 : How To Find Slope By Graphing Functions

Find the slope of the line tangent to h(x), when .

Explanation:

Find the slope of the line tangent to h(x), when .

To find the slope of a tangent line, we need to find the derivative of our function:

Begin by recalling the rule for polynomial derivatives, derivative of sine, and derivative of

Polynomials derivatives are found by decreasing our exponent by one, and then dividing by that number.

The derivative of sine is cosine

The derivative of  is

So with that in mind, let's find h'(x)

Next, we need to find h'(0), so plug in 0 for x and simplify:

So our slope is 0 when x=0.

### Example Question #28 : How To Find Slope By Graphing Functions

Find the slope of the line tangent to f(x) when x is -5.

Explanation:

Find the slope of the line tangent to f(x) when x is -5.

To find the slope of a tangent line, first find the derivative. Then, plug in the given point. Recall the power rule of derivatives. (Multiply each term by its exponent, then subtract one from the exponent)

Becomes:

Next, plug in -5

In doing so, we arrive at -112530, a very steep slope indeed!

### Example Question #29 : How To Find Slope By Graphing Functions

If the equation for a graph given is , find the slope of a line tangent to this graph at .

None of the above.

Explanation:

In order to find the slope, you take derivative of the graph equation.  Then by plugging in any  value, you can find the slope of the graph.

In order to take the derivative of equation, the power rule must be applied, .  You must also apply the quotient rule .

Taking the derivative of the graph equation

937,500+125-160

Plugging in , you find the slope to be .

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