Check sibling questions

Ex 6.2, 5 - Find intervals where f(x) = 2x^3 - 3x^2 - 36x + 7 is

Ex 6.2, 5 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.2, 5 - Chapter 6 Class 12 Application of Derivatives - Part 3


Transcript

Ex 6.2, 5 Find the intervals in which the function f given by f (𝑥) = 2𝑥3 – 3𝑥2 – 36𝑥 + 7 is (a) strictly increasing (b) strictly decreasingf(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)

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.