ch 6 hw 2 question 11 of 23 (1 point) | question attempt 1 of unlimited part 1 of 4 (a) over what…

ch 6 hw 2 question 11 of 23 (1 point) | question attempt 1 of unlimited part 1 of 4 (a) over what interval(s) does the depth increase? write your answer in interval notation. depth of the retention pond is increasing on the interval (4,6) u (8,10). correct answer: (4,6) u (9,10) part 2 of 4 (b) over what interval(s) does the depth decrease? write your answer in interval notation. depth of the retention pond is decreasing on the interval (0,4) u (6,9). part 3 of 4 (c) estimate the times and values of any relative maxima or minima on the interval (0,10). at t = 4 and 9, the function has a relative minimum of 1.5 and 1.75, respectively. part: 3 / 4 part 4 of 4 at t =, the function has a relative maximum of on the interval (0,10).

ch 6 hw 2 question 11 of 23 (1 point) | question attempt 1 of unlimited part 1 of 4 (a) over what interval(s) does the depth increase? write your answer in interval notation. depth of the retention pond is increasing on the interval (4,6) u (8,10). correct answer: (4,6) u (9,10) part 2 of 4 (b) over what interval(s) does the depth decrease? write your answer in interval notation. depth of the retention pond is decreasing on the interval (0,4) u (6,9). part 3 of 4 (c) estimate the times and values of any relative maxima or minima on the interval (0,10). at t = 4 and 9, the function has a relative minimum of 1.5 and 1.75, respectively. part: 3 / 4 part 4 of 4 at t =, the function has a relative maximum of on the interval (0,10).

Answer

Explanation:

Step1: Identify increasing - decreasing intervals

A function is increasing when the graph goes up from left - to - right and decreasing when it goes down. From the graph, we can see the depth increases when the curve rises.

Step2: Analyze relative extrema

A relative minimum is a point where the function changes from decreasing to increasing, and a relative maximum is a point where the function changes from increasing to decreasing. For part (a), the depth of the retention pond is increasing on the interval $(4,6)\cup(9,10)$. For part (b), the depth of the retention pond is decreasing on the interval $(0,4)\cup(6,9)$. For part (c), at $t = 4$ and $t=9$, the function has relative minima of approximately $1.5$ and $1.75$ respectively. For part (d):

Step3: Locate relative maximum

We observe the graph. The function changes from increasing to decreasing at $t = 6$. The value of the function (depth) at $t = 6$ is approximately $2.25$.

Answer:

At $t = 6$, the function has a relative maximum of $2.25$ on the interval $(0,10)$.