Which of the following statements are true :

Maths Differentiation and Applications of Derivatives General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If f(x) is differentiable function such that f(a) ≠ f(b) then there exist no c ∈ (a, b) such that f’

The function x 100 + sinx – 1 is strictly increasing in [0, 1]

= 0 If a, b, c are in A.P, then at least one root of the equation 3ax 2 – 4bx + c = 0 is positive

The number of solution(s) of equation 3 tanx + x 3 = 2 in (0, π /4) is 2

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(b,c) let f(x) = tan –1 x

f’(x) =

∴ |f ′ | = < 1

< 1

Let f(x) = x 100 + sin x – 1

f ′ (x) = 100x 99 + cosx > 0, x ∈ [0, 1]

⇒ f(x) is increasing.

Suppose f(x) = ax 3 – 2bx 2 + cx, then clearly f(0) = 0

and f(1) = a – 2b + c = 0,

 f(0) = f(1) ∴ By Rolle’s theorem f ′ (x) = 3ax 2 – 4bx + c = 0

for atleast one x in (0, 1) which is positive

f(x) = 3 tanx + x 3 – 2 ⇒ f ′ (x) = 3sec 2 x + 3x 2 > 0 ⇒ f(x) is always increasing

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