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 of
between 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