# Precalculus : Tangents To a Curve

## Example Questions

2 Next →

### 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 .

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

### 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 .

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

### 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 .

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 →