`f(x) = -1/2 + (7/5)x^3, (0,-1/2)` 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.

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Textbook Question

Chapter 2, 2.2 - Problem 33 - 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 for the derivative function.

`f'(x)= 21/5 x^2`

Substitute the point where x=0 to find the slope at that point.

`f'(x)= 21/5 (0)^2= 0`

The slope at that point is zero.

Graph the original function.

Graph the derivative function.

We can then see that we have a horizontal slope at x=0.

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