Provide an appropriate response.Let f(x) = (x - 8)2/3 (a) Does f'(8) exist? (b) Show that the only local extreme value of f occurs at x = 8. (c) Does the result of (b) contradict the Extreme Value Theorem? (d) Repeat parts (a) and (b) for f(x) = (x - c)2/3.Give reasons for your answers.
What will be an ideal response?
(a) No, since f'(x) = 
(x - 8)-1/3, which is undefined at x = 8.
(b) The derivative is defined and nonzero for all x ? 8.
(c) No, f(x) need not have a global maximum because its domain is all real numbers. Any restriction of f to a closed interval of the form [a, b] would have both a maximum value and a minimum value on the interval.
(d) The answers are the same as (a) and (b) with 8 replaced by c.
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A. 32?
B. 
?
C. 12?
D. 16?
Solve the problem.A rare species of insect was discovered in the rain forest of Costa Rica. Environmentalists transplant the insect into a protected area. The population of the insect t months after being transplanted is P(t) = 
.a) What was the population when t = 0?b) What will the population be after 10 years?c) What is the largest value the population could reach?
What will be an ideal response?
Find the surface area of a cylinder with radius 4.6 mm and height 9.2 mm. Round the answer to one decimal place.
(a) 133.0 mm² (b) 265.9 mm² (c) 294.6 mm² (d) 398.9 mm²
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A. x = -16 B. x = 16 C. x = -22 D. x = 22