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

5-55.

Draw the graph of $f ( x ) = \sqrt { x } \operatorname { cos } x$ for $0 ≤ x ≤ 3$

1. Find $f^\prime(x)$.

2. Graph $f^\prime(x)$ using your graphing calculator. Then, use this graph to find the $x$-value of the local maximum of $f(x)$.

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

3. Likewise, use a graph of $f^{\prime\prime}(x)$ to find the point of inflection of $f ( x ) = \sqrt { x } \operatorname { cos } x$ between $0 ≤ x ≤ 3$.

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

Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: Calc 5-55 HW eTool