the graph of a function f is given. use the graph to find each of the following.\na. the numbers, if any, at…

Explanation:

Step1: Identify relative maxima

Relative maxima occur where the function changes from increasing to decreasing. Looking at the graph, we see the function has relative maxima at $x = - 1$ and $x = 2$. The $y$-values at these points are $y = 3$.

Step2: Identify relative minima

Relative minima occur where the function changes from decreasing to increasing. From the graph, the function has a relative minimum at $x = 1$ and the $y$-value at this point is $y = 1$.

Answer:

a. The numbers at which $f$ has a relative maximum are $x=-1$ and $x = 2$. The relative maxima are $y = 3$. b. The number at which $f$ has a relative minimum is $x = 1$. The relative minimum is $y = 1$.