Question

Question #07ee7

Answer 1

12

Explanation:

Recall that for a given `f(x)`, `f'(x)` is the equation for the slope of the tangent line. We are given two points on a tangent line, so we can use the formula for slope to find the `f'` here.

`m = (y_2-y_1)/(x_2-x_1) = (-32-4)/(5-8) = (-36)/(-3) = 12 = f'(8)`

Thus, `f'(8) = 12`

Please note that `f'(x)` measures the slope of the tangent line; it does not provide the entire equation for the tangent line. To find that we would have to use `f'(8)` in point-slope form. That is beyond the scope of this problem.