Calculus of a Single Variable, Chapter 2, 2.2, Section 2.2, Problem 36

Take the derivative of the given function. The chain rule will be shown in the steps. The derivative of the inner function (x-4) with the respect to x is 1.
f'(x) =2 * 2(x-4)^(2-1) * (1)
Simplify.
f'(x) =4(x-4) = 4x-16
Substitute the x value of the given point to find the slope at that point.
f'(2) = 4(2)-16
The answer is:
f'(2) = -8
We can graph the derivative function to show that we have a slope of negative eight at x=2.