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 Dec. 16, 2024 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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