Let f(x) = 8(x-6)^(2/3) + 8
A) Find all critical values
B) Where is f(x) increasing?
C) Where is f(x) decreasing?
D) List the x values of all local maxima of f
E) List the x values of all local minima of f
Differentiate: f ' (x) = (16/3) (x - 6)^(-1/3)
A) x = 6 (at this point the denominator is zero, the derivative does not exist)
B) f '(x) > 0 if x > 6, so the function increases for 6 < x < +infty
C) f '(x) < 0 if x < 6, so the function decreases for -infty < x < 6
D) There is no local maximum for this function, it goes to infinity with |x|.
E) The local minimum is at x = 6 (the derivative changes its sign from - to + at this point) where the function value is f(6) = 8.
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