question 26 of 47 (1 point) | question attempt: 1 of 1 use the graph to answer the following questions. (a)…

question 26 of 47 (1 point) | question attempt: 1 of 1 use the graph to answer the following questions. (a) over which intervals is the function increasing? choose all that apply. (-∞, -9) (-6, -3) (1, 5) (5, 8) (1, 8) (8, ∞) (b) at which x - values does the function have local maxima? if there is more than one value, separate them with commas.
Answer
Explanation:
Step1: Recall increasing - function definition
A function is increasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, we have $f(x_1)<f(x_2)$. Looking at the graph, we can see the function is increasing on the intervals where the graph is going up as we move from left - to - right.
Step2: Identify increasing intervals
From the graph, the function is increasing on the intervals $(-6,-3)$ and $(1,5)$.
Step3: Recall local maxima definition
A local maximum occurs at a point $x = c$ if $f(c)\geq f(x)$ for all $x$ in some open interval containing $c$.
Step4: Identify local maxima $x$ - values
From the graph, the local maxima occur at $x=-9, - 2,6$.
Answer:
(a) $(-6,-3),(1,5)$ (b) $-9,-2,6$