`f(x) = 2(x-4)^2, (2,8)` Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

Expert Answers
kalau eNotes educator| Certified Educator

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)`


`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.