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NCERT Class 12 Maths Chapter 6: Applications Of Derivatives 19 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 6 Applications Of Derivatives — Exercise 6.2

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Show f(x)=\(3 x + 17\) is increasing on R.

Show f(x)=\(e^{2 x}\) is increasing on R.

Show sin x is (a) increasing on (0,π/2), (b) decreasing on (π/2,π), and (c) neither on (0,π).

Find intervals of increase and decrease for f(x)=\(2 x^{2} - 3 x\).

Find intervals of increase and decrease for f(x)=\(2 x^{3} - 3 x^{2} - 36 x + 7\).

Find intervals of strict increase/decrease: (a) \(x^{2} + 2 x - 5\); (b) \(- 2 x^{2} - 6 x + 10\); (c) \(- 2 x^{3} - 9 x^{2} - 12 x +…

Prove log(1+x)−2x/(2+x) is increasing for x>−1.

Find intervals of increase and decrease for f(x)=\(x^{2} \left(x - 2\right)^{2}\).

Prove 4sin θ/(2+cos θ)−θ is increasing on [0,π/2].

Prove the logarithmic function is increasing on (0,∞).

Prove f(x)=x²−x+1 is neither strictly increasing nor decreasing on (−1,1).

Which are decreasing on (0,π/2): (A) cos x, (B) cos 2x, (C) cos 3x, (D) tan x?

On which option interval is f(x)=x¹⁰⁰+sin x−1 decreasing?

For which a is f(x)=x²+ax+1 increasing on [1,2]?

If interval I is disjoint from [−1,1], prove f(x)=x+1/x is increasing on I.

Prove log(sin x) increases on (0,π/2) and decreases on (π/2,π).

Prove log|cos x| decreases on (0,π/2) and increases on (3π/2,2π).

Prove f(x)=x³−3x²+3x−100 is increasing on R.

On which interval is y=x²e^(−x) increasing?