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 Sept. 4, 2021 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 a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
Hi, it looks like you're using AdBlock :(
Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.
Please login to view more pages. It's free :)
Teachoo gives you a better experience when you're logged in. Please login :)
