`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.

Textbook Question

Chapter 2, 2.2 - Problem 36 - Calculus of a Single Variable (10th Edition, Ron Larson).
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kalau | (Level 2) Adjunct Educator

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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.

 

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