### Home > APCALC > Chapter 5 > Lesson 5.2.1 > Problem5-55

5-55.

Draw the graph of $f(x) = \sqrt{x}\operatorname{cos}(x)$ for $0 ≤ x ≤ 3$. 5-55 HW eTool (Desmos). Homework Help ✎

1. Write an equation for $f^\prime$.

2. Graph $y = f^\prime(x)$ using your graphing calculator. Then, use this graph to locate the x‑value of the local maximum of f over $0 ≤ x ≤ 3$.

The location of a local maximum on f(x) can be found where f '(x) = 0 AND changes from positive values to negative values.

3. Likewise, use a graph of $y = f ^{\prime\prime}(x)$ to locate the point of inflection of $f$ for $0 ≤ x ≤ 3$.

A zero on the second derivative that crosses the x-axis (or changes sign) indicates a point of inflection on the original function.

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