increasing and decreasing functions\ndetermine the intervals for which the function is increasing or…

increasing and decreasing functions\ndetermine the intervals for which the function is increasing or decreasing. determine any relative extrema.\nnote: you will need to estimate some answers. give estimates with at least one decimal place.\nincreasing:\ndecreasing:\nlocal max = at x =\nlocal min = at x =

increasing and decreasing functions\ndetermine the intervals for which the function is increasing or decreasing. determine any relative extrema.\nnote: you will need to estimate some answers. give estimates with at least one decimal place.\nincreasing:\ndecreasing:\nlocal max = at x =\nlocal min = at x =

Answer

Explanation:

Step1: Identify increasing intervals

A function is increasing when the graph goes up from left - to - right. By observing the graph, the function is increasing on the interval $(-4,1)$.

Step2: Identify decreasing intervals

A function is decreasing when the graph goes down from left - to - right. The function is decreasing on the intervals $(-\infty,-4)$ and $(1,\infty)$.

Step3: Find local maxima

A local maximum occurs where the function changes from increasing to decreasing. From the graph, the local maximum value is approximately $y = 1$ and it occurs at $x=1$.

Step4: Find local minima

A local minimum occurs where the function changes from decreasing to increasing. The local minimum value is approximately $y=-5$ and it occurs at $x = - 4$.

Answer:

Increasing: $(-4,1)$ Decreasing: $(-\infty,-4),(1,\infty)$ Local Max = $1$ at $x = 1$ Local Min = $-5$ at $x=-4$