Solve the problem.Give reasons for your answers.Let f(x) = (x - 2)2/3 (a) Does f'(2) exist?(b) Show that the only local extreme value of f occurs at x = 2.(c) Does the result of (b) contradict the Extreme Value Theorem?(d) Repeat parts (a) and (b) for f(x) = (x - c)2/3.
What will be an ideal response?
(a) No, since f'(x) = 
(x - 2)-1/3, which is undefined at x = 2.
(b) The derivative is defined and nonzero for all x ? 2.
(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 2 replaced by c.
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Find an equation that shifts the graph of f by the indicated amounts.f(x) = x4; right 6 units, up 2 units
A. y = (x - 6)4 + 2 B. y = - (x - 6)4 + 12 C. y = (x + 6)4 - 2 D. y = - (x - 6)4 + 2
If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."{(-2, 4), (2, -4), (8, -2), (-8, 2)}
A. {(4, -2), (-4, 2), (-2, 8), (2, -8)} B. {(4, -2), (-4, 2), (-2, -8), (2, 8)} C. {(4, -2), (-4, 2), (8, -2), (2, -8)} D. Not one-to-one
Solve the problem.The sales for a gaming console for various years are listed in the table below. 
Let f(t) represent the sales (in billions of dollars) at t years since 2008. A reasonable model is 
Use the model to predict when the sales will be $10 billion.
A. 2028 B. 2025 C. 2026 D. 2027
Write the complex conjugate.11
A. -11 B. -11i C. 11i D. 11