# Precalculus : Tangents To a Curve

## 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 2 Next →

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