Discuss the applicability of Rolle’s Theorem for the following funct

1.	Discuss the applicability of Rolle’s Theorem for the following functions on the indicated intervals: f(x) = 2x2 – 5x + 3 on [1, 3]
Answer» Given as function is f(x) = 2x² – 5x + 3 on [1, 3] Here, the given function f is a polynomial. Therefore, it is continuous and differentiable everywhere. Then, let us find the values of function at the extreme values. ⇒ f (1) = 2(1)²– 5(1) + 3 ⇒ f (1) = 2 – 5 + 3 ⇒ f (1) = 0…… (1) ⇒ f (3) = 2(3)²– 5(3) + 3 ⇒ f (3) = 2(9) – 15 + 3 ⇒ f (3) = 18 – 12 ⇒ f (3) = 6…… (2) From the equation (1) and (2), we can say that, f(1) ≠ f (3) Therefore, Rolle’s Theorem is not applicable for the function f in interval [1, 3].

Discuss the applicability of Rolle’s Theorem for the following functions on the indicated intervals: f(x) = 2x2 – 5x + 3 on [1, 3]

Answer»

Given as function is f(x) = 2x² – 5x + 3 on [1, 3]

Here, the given function f is a polynomial. Therefore, it is continuous and differentiable everywhere.

Then, let us find the values of function at the extreme values.

⇒ f (1) = 2(1)²– 5(1) + 3

⇒ f (1) = 2 – 5 + 3

⇒ f (1) = 0…… (1)

⇒ f (3) = 2(3)²– 5(3) + 3

⇒ f (3) = 2(9) – 15 + 3

⇒ f (3) = 18 – 12

⇒ f (3) = 6…… (2)

From the equation (1) and (2), we can say that, f(1) ≠ f (3)

Therefore, Rolle’s Theorem is not applicable for the function f in interval [1, 3].