Question

the graph of the polynomial function g is shown. the function f is defined for 0 < x ≤ 3 and is identical to the function g on that interval. how many total local minima and local maxima does the function f have? a. two b. four c. five d. seven

Explanation:

Step1: Recall local extrema definition

Local maxima and minima occur where the function changes from increasing to decreasing or vice - versa.

Step2: Analyze the graph in the interval $0\leq x\leq3$

By observing the graph of $g$ (and since $f$ is identical to $g$ in $0\leq x\leq3$), we count the number of times the function changes its direction of increase and decrease. In the given interval, we can see that the function has 2 local minima and 2 local maxima.

Answer:

B. Four