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

5-55.

Draw the graph of

for 0 ≤ *x*≤ 3. Homework Help ✎Find

*f*′(*x*).Graph

*f*′(*x*) using your graphing calculator. Then, use this graph to find the*x*-value of the local maximum of*f*(*x*).Likewise, use a graph of

*f*″(*x*) to find the point of inflection ofbetween 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.

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