Consider the function h(x) = 1/5 x^5 − 1/3 x^3 + 2. a)  Using derivatives, find the interval(s) where ℎ is increasing and the interval(s) where h is decreasing. b)  Using the second derivative test, determine the location of each local maximum or minimum. c) Sketch the graph of y = h(x) using the data you gathered in parts a) and b).

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Q: In Exercises 13–24, compute the derivative using derivative rules that have been introduced so far.

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Q: In Exercises 13–24, compute the derivative using derivative rules that have been introduced so far.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: