Precalculus : Tangents To a Curve

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #6 : Find The Equation Of A Line Tangent To A Curve At A Given Point

Write the equation for the tangent line to at .

Possible Answers:

Correct answer:

Explanation:

First, find the slope of the tangent line by taking the first derivative:

To finish determining the slope, plug in the x-value, 2:

the slope is 6

Now find the y-coordinate where x is 2 by plugging in 2 to the original equation:

To write the equation, start in point-slope form and then use algebra to get it into slope-intercept like the answer choices.

distribute the 6

add 8 to both sides

Example Question #7 : Find The Equation Of A Line Tangent To A Curve At A Given Point

Write the equation for the tangent line for at .

Possible Answers:

Correct answer:

Explanation:

First, take the first derivative in order to find the slope:

 

To continue finding the slope, plug in the x-value, -2:

Then find the y-coordinate by plugging -2 into the original equation:

The y-coordinate is

Now write the equation in point-slope form then algebraically manipulate it to match one of the slope-intercept forms of the answer choices.

distribute the -5

add to both sides

 

 

Example Question #8 : Find The Equation Of A Line Tangent To A Curve At A Given Point

Write the equation for the tangent line to at .

Possible Answers:

Correct answer:

Explanation:

First distribute the . That will make it easier to take the derivative:

Now take the derivative of the equation:

To find the slope, plug in the x-value -3:

To find the y-coordinate of the point, plug in the x-value into the original equation:

Now write the equation in point-slope, then use algebra to get it into slope-intercept like the answer choices:

 distribute

subtract from both sides

write as a mixed number

 

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