this is section 3.7 problem 4: the function h is represented by the graph in the textbook. use the graph to…

this is section 3.7 problem 4: the function h is represented by the graph in the textbook. use the graph to find the absolute maximum and minimum values, if exist, on the given interval. the answers should either be an integer or an integer and a half such as \1.5\. use \dne\ if it does not exist. (a) on interval (-3, -0.5), absolute maximum = dne, absolute minimum = -1 at x = -3 (b) on interval 0, 2), absolute maximum = , absolute minimum = at x = (c) on interval (0, 3), absolute maximum = at x = , absolute minimum = at x = (d) on interval (-2, 0, absolute maximum = at x = , absolute minimum = at x = hint: refer to the figures in the textbook. symbolic formatting help

this is section 3.7 problem 4: the function h is represented by the graph in the textbook. use the graph to find the absolute maximum and minimum values, if exist, on the given interval. the answers should either be an integer or an integer and a half such as \1.5\. use \dne\ if it does not exist. (a) on interval (-3, -0.5), absolute maximum = dne, absolute minimum = -1 at x = -3 (b) on interval 0, 2), absolute maximum = , absolute minimum = at x = (c) on interval (0, 3), absolute maximum = at x = , absolute minimum = at x = (d) on interval (-2, 0, absolute maximum = at x = , absolute minimum = at x = hint: refer to the figures in the textbook. symbolic formatting help

Answer

Explanation:

Step1: Analyze interval (-3, -0.5)

From the graph, in the open - interval (-3, -0.5), the function is decreasing. The absolute maximum does not exist as the interval is open and the function continues to decrease towards the left - hand side of the interval. The absolute minimum value occurs near the right - hand side of the interval. By observing the graph, the absolute minimum value is approximately - 1 at (x=-0.5) (closest to the right - hand side of the open interval).

Step2: Analyze interval [0, 2)

In the half - open interval [0, 2), by observing the graph, the function first decreases and then increases. The absolute minimum value is the value of the function at the local minimum point within the interval. The absolute minimum value is 0 at (x = 1). The absolute maximum does not exist in the half - open interval [0, 2) as the function is increasing as (x) approaches 2 from the left and the interval is open at (x = 2).

Step3: Analyze interval (0, 3)

In the open interval (0, 3), the function has a local minimum and then increases. The absolute minimum value is 0 at (x = 1). The absolute maximum value occurs at (x=3) (but since the interval is open at (x = 3), we look at the behavior of the function as (x) approaches 3 from the left). The absolute maximum value is 4 at (x) close to 3 from the left.

Step4: Analyze interval (-2, 0]

In the half - open interval (-2, 0], by observing the graph, the function is increasing. The absolute minimum value is the value of the function at (x=-2), which is - 2. The absolute maximum value is 0 at (x = 0).

Answer:

(a) absolute minimum = -1, at (x=-0.5); absolute maximum = DNE (b) absolute minimum = 0, at (x = 1); absolute maximum = DNE (c) absolute minimum = 0, at (x = 1); absolute maximum = 4, at (x) close to 3 from the left (d) absolute minimum = -2, at (x=-2); absolute maximum = 0, at (x = 0)