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 (local max) or decreasing to increasing (local min).

Step2: Examine the graph on $0\leq x\leq3$

On the interval $0\leq x\leq3$, observe the turning - points of the graph of $f$ (which is the same as $g$ on this interval). We can see that there are 2 local minima and 3 local maxima.

Step3: Calculate the total number

Add the number of local minima and local maxima: $2 + 3=5$.

Answer:

C. Five