Let f be the function defined by the piecewise function:

Question

f(x) = x^3 for x less than or equal to 0
x for x greater than 0
Which of the following is true?

a) f is an odd function
b) f is discontinuous at x=0
c) f has a relative maximum
d) f'(0) = 0
e) f'(x) > 0 for (x is not 0)

I strongly believe that a, b, and c are not the correct answer.

Answer 1

I think it would be e considering the fact that when you take the derivative, you get 3x^2 and 1, an when you input zero for both of these, there is a jump discontinuity. Is this right?

Answer 2

I agree with e