Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 03/Solution 1

Graph of $f$, with the graph of its derivative overlayed in red.

The graph of $f'$ is pictured in red, on top of the graph of $f$.

The essential aspect is that the derivative is 0 (or intersects the $x$-axis) at every $x$ for which the original function attains a local minimum or maximum, and the derivative is positive or negative (is above or below the $x$-axis) at every $x$ for which the original function is increasing or decreasing, respectively.