Question 26 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards
Last updated at August 14, 2026 by Teachoo
The real function
f
(x) = 2x3 – 3x2 – 36x + 7 is:
(a) Strictly increasing in (−∞,−2) and strictly decreasing in ( −2, ∞)
(b) Strictly decreasing in (−2, 3)
(c) Strictly decreasing in (−∞, 3) and strictly increasing in (3, ∞)
(d) Strictly decreasing in (−∞,−2) ∪ (3, ∞)
Question 26 The real function f (x) = 2x3 – 3x2 – 36x + 7 is: (a) Strictly increasing in (−∞,−2) and strictly decreasing in ( −2, ∞) (b) Strictly decreasing in (−2, 3) (c) Strictly decreasing in (−∞, 3) and strictly increasing in (3, ∞) (d) Strictly decreasing in (−∞,−2) ∪ (3, ∞)
f(𝑥) = 2𝑥3 – 3𝑥2 – 36𝑥 + 7
Calculating f’(𝒙)
f’(𝑥) = 6𝑥2 – 6𝑥 – 36 + 0
f’(𝑥) = 6 (𝑥2 – 𝑥 – 6 )
f’(𝑥) = 6(𝑥^2 – 3𝑥 + 2𝑥 – 6)
f’(𝑥) = 6(𝑥(𝑥 − 3) + 2 (𝑥 − 3))
f’(𝒙) = 6(𝒙 – 3) (𝒙 + 2)
Putting f’(x) = 0
6(𝑥+2)(𝑥 –3)=0
(𝑥+2)(𝑥 –3)=0
So, x = −2 and x = 3
Plotting points on number line
Hence,
f is strictly increasing in (−∞ ,−𝟐) & (𝟑 ,∞)
f is strictly decreasing in (−𝟐, 𝟑)
So, the correct answer is (D)
Made by
Davneet Singh
Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.
Many students prefer Teachoo Black for a smooth, ad-free learning experience.
Go ad-free with Teachoo Black
Adblock detected
Skip every ad. Keep every answer.
Teachoo Black gives you a clean, uninterrupted study experience on every page.
You are here
