Question

Verify the Rolle’* Theorem for functions on the indicated intervals: f(x) = x2 – 5x + 4 on [0, π/6]

Answer 1

Given as the function is f (x) = x2 – 5x + 4 on [1, 4]

Here, given function f is a polynomial it is continuous and differentiable everywhere i.e., on R.

Let'* find the values at extremes

⇒ f (1) = 12 – 5(1) + 4

⇒ f (1) = 1 – 5 + 4

⇒ f (1) = 0

⇒ f (4) = 42 – 5(4) + 4

⇒ f (4) = 16 – 20 + 4

⇒ f (4) = 0

f(1) = f(4). Therefore, there exists a c ϵ (1, 4) such that f’(c) = 0.

Let us find the derivative of f(x):

Thus, Rolle'* theorem is verified.