Consider the function f(x) = 3-3 x^{2/3} on the interval [ -1 , 1 ].

Question

Which of the three hypotheses of Rolle's Theorem fails for this function on the inverval?

(a) f(x) is continuous on [-1,1].
(b) f(x) is differentiable on (-1,1).
(c) f(-1)=f(1).

Answer:( a, b, or c )

Answer 1

dy/dx = -3*(2/3)x^-(2/3) =-2/x^(2/3)
which is undefined at x = 0