Question

For y = -x^2 + 2x there exist a c in the interval [- 19765, 19767] Such that f'(c) = 0.

(a) True

(b) False

The question was posed to me in homework.

Asked question is from Rolle’s Theorem topic in section Differential Calculus of Engineering Mathematics

Answer 1

The correct choice is (a) True

Easiest explanation: The key here is to rewrite the function as y = -(x – 1)^2 + 1

Observe here that on substituting – 19765 and 19767 in the equation we get

(-19766)^2 + 1 and (-19766)^2 + 1 respectively.

 As we are dealing with their squared values they have to be equal

We have

f(-19765) = f(19767)

Polynomial functions are continuous and differentiable over the whole domain and hence by Rolles Theorem we must have a c such that f'(c) = 0 in the interval [-19765, 19767]

Hence, the claim is true.