Jake F.

The function f(x) = x^(2/3) on [-8,8] does not satisfy the conditions of the Mean Value Theorem because...

(A) f(0) is not defined

(B) f(x) is not continuous on [-8,8]

(C) f '(-1) does not exist

(D) f(x) is not defined for x<0

(E) f '(0) does not exist

I know that A, C, and D are false since all of the points on [-8,8] are defined. My book says the answer is E, which is true, but isn't B also true because f(0) is a cusp, so there is no derivative there making the function not continuous? Any help would be greatly appreciated. :)

How would you differentiate this?

x + cos (x + y) = 0

I know you have to differentiate with respect to x and y, then rearrange the parts to get dy/dx, but I'm not sure how to do this in this problem because of the (x + y). Any help would be greatly appreciated. :)