208k views
3 votes
APCAL AB!!!!!!!!!!!!!!!!!

APCAL AB!!!!!!!!!!!!!!!!!-example-1
User Chris Gibb
by
7.1k points

1 Answer

3 votes

Answer:


y=-10x+89

Explanation:

Remember that the derivative tells us the slope of the tangent line at a given point.

So, we want to find the equation of the tangent line to f(x) at x=8.

We are given that f'(8) is -10.

In other words, the slope of the tangent line to f(x) at x=8 is -10.

We also know that f(8)=9. In other words, we have the point (8,9).

So, we can use the point-slope form to figure out the equation:


y-y_1=m(x-x_1)

Substitute -10 for m and let (8,9) be (x₁, y₁). So:


y-9=-10(x-8)

Distribute the -10:


y-9=-10x+80

Add 9 to both sides:


y=-10x+89

And we're done!

User Elisia
by
7.2k points