`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.
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.