the graph of a function f is given. use the graph to estimate the following. (a) all the local maximum and…

the graph of a function f is given. use the graph to estimate the following. (a) all the local maximum and minimum values of the function and the value of x at which each occurs. local maximum (x, y) = local minimum (x, y) = (smaller x - value) local minimum (x, y) = (larger x - value) (b) the intervals on which the function is increasing and on which the function is decreasing. (enter your answers using interval notation.) increasing decreasing

the graph of a function f is given. use the graph to estimate the following. (a) all the local maximum and minimum values of the function and the value of x at which each occurs. local maximum (x, y) = local minimum (x, y) = (smaller x - value) local minimum (x, y) = (larger x - value) (b) the intervals on which the function is increasing and on which the function is decreasing. (enter your answers using interval notation.) increasing decreasing

Answer

Explanation:

Step1: Identify local maximum

A local maximum occurs where the function changes from increasing to decreasing. By observing the graph, the local - maximum point is at $(0, 4)$.

Step2: Identify local minima

Local minima occur where the function changes from decreasing to increasing. The smaller $x$ - value local minimum is at $(-2,-2)$ and the larger $x$ - value local minimum is at $(2,2)$.

Step3: Determine increasing intervals

The function is increasing when the $y$ - values are getting larger as $x$ increases. From the graph, the increasing intervals are $(-2,0)\cup(2,\infty)$.

Step4: Determine decreasing intervals

The function is decreasing when the $y$ - values are getting smaller as $x$ increases. From the graph, the decreasing intervals are $(-\infty,-2)\cup(0,2)$.

Answer:

(a) local maximum $(x,y)=(0,4)$ local minimum $(x,y)=(-2,-2)$ (smaller $x$ - value) local minimum $(x,y)=(2,2)$ (larger $x$ - value) (b) increasing: $(-2,0)\cup(2,\infty)$ decreasing: $(-\infty,-2)\cup(0,2)$