Question

verify rolle's theorem for function f(x) = x^2-1 in the interval [ -1,1 ]​

Answer 1

(i). Since, x^2 - 1 is a polynomial function, so it is continuous at [-1,1]

(ii). So it is differentiable also at (-1,1)

(iii ). f (x) = x^2 - 1

f (a) = (-1)^2 - 1 = 1 - 1 = 0

f (b) = 1^2 - 1 = 0

Then, there exists at least one real number c€(a, b) such that f'(c) = 0.

f'(c) = 2c = 0

c = 0 € ( - 1,1)

Hence, Rolle's theorem is verified.

Answer 2

Answer:

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