Question

APCAL AB!!!!!!!!!!!!!!!!!

Answer 1

Answer:

$y=-10x+89$

Step-by-step 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!