Need calculus help with critical values

Calculus
Tutor: None Selected Time limit: 1 Day

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

Apr 8th, 2015

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.


Apr 8th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Apr 8th, 2015
...
Apr 8th, 2015
May 22nd, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer