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2 answers:
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Answer:
a. Local maximum = 50 units per week.
b. The graph is never concave upward.
c. (0, 80)
Step-by-step explanation:
a. The revenue function is:
The derivate of the revenue function for which R'(x) = 0 gives us the local extrema:
The second derivate of the revenue function determines if x =50 is local maximum or minimum:
Since the second derivate yields a negative value, x = 50 units per week is a local maximum.
b. Since there are no local minimums in the range of 0 < x < 80, the graph is never concave upward.
c. Since there is only one local maximum in the range of 0 < x < 80, the graph is concave downward from x>0 to x<80 or (0, 80)