Question

(i) Find if x = a(t – sin t) y = a(1 + cos t)

(ii) Verify Rolles theorem for the function f(x) = x² + 2 in the interval [-2, 2] 
 

Answer 1

(ii) f(x) = x² + 2, f'(x) = 2x.

As f is a polynomial, it is continuous in the interval [-2,2] and differentiable in the interval (-2,2)

f(-2) = 4 + 2 = 6

f(2) = 4 + 2 = 6

f'(c) = 0 ⇒ 2c = 0 ⇒ c = 0 ∈ (-2,2)

Hence Rolle's Theorem is verified.