Refer to the graph to answer each of the following questions. For parts (A) and

Question

Refer to the graph to answer each of the following questions. For parts (A) and (B), use interval notation to report your answer. (If needed, you use U for the union symbol.)

(A) For what values of x in (0,8) is f(x) increasing? (If the function is not increasing anywhere, enter None .)

(B) For what values of x in (0,8) is f(x) concave down? (If the function is not concave down anywhere, enter None .)

(C) Find all values of x in (0,8) is where f(x) has a local minimum, and list them (separated by commas) in the box below. (If there are no local minima, enter None .)

(D) Find all values of x in (0,8) is where f(x) has an inflection point, and list them (separated by commas) in the box below. (If there are no inflection points, enter None .)

Below is the graph of the derivative f?(x) of a function defined on the interval (0,8). Refer to the graph to answer each of the following questions. For parts (A) and (B), use interval notation to report your answer. (If needed, you use U for the union symbol.) For what values of x in (0,8) is f(x) increasing? (If the function is not increasing anywhere, enter None .) For what values of x in (0,8) is f(x) concave down? (If the function is not concave down anywhere, enter None .) Find all values of x in (0,8) is where f(x) has a local minimum, and list them (separated by commas) in the box below. (If there are no local minima, enter None .) Find all values of x in (0,8) is where f(x) has an inflection point, and list them (separated by commas) in the box below. (If there are no inflection points, enter None .)

Explanation / Answer

A) A function is increasing if its derivative is positive.

from the graph, f'(x) > 0 when 0 < x < 3 and 5 < x < 8

B) A function is concave down when its second derivative is negative

from the graph, f''(x) < 0 when 2 < x < 4 and 6 < x < 8

C) A function has a local minimum if its derivative is equal to 0

from the graph f'(x) = 0 when x = 3, and x = 5

D) A function has a an inflection point when its second derivative equals 0

from the graph, f''(x) = 0 when x = 2, x = 4 , and x = 6

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