Q. 6 C

Find the intervals in which the following functions are strictly increasing or decreasing:–2x3 – 9x2 – 12x + 1

It is given that function f(x) = –2x3 – 9x2 – 12x + 1

f’(x) = -6x2 – 18x + 12

f’(x) = -6(x2 +3x + 6)

f’(x) = -6(x + 1)(x + 2)

If f’(x) = 0, then we get,

x = -1 and -2

So, the points x = -1 and x = -2 divides the real line into two disjoint intervals,

(-∞,-2), (-2,-1) and (-1,∞)

So, in interval (-∞,-2),(-1,∞)

f’(x) = -6(x + 1) (x +2) < 0

Therefore, the given function (f) is strictly decreasing for x < -2 and x>-1.

So, in interval (-2.-1)

f’(x) = -6(x + 1)(x+2) > 0

Therefore, the given function (f) is strictly increasing for -2 < x < -1.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
How to find Maxima & Minima?43 mins
Tangent & Normal To A Curve53 mins
Test your knowledge of Tangents & Normals (Quiz)52 mins
Interactive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minima48 mins
Tangents & Normals (Concept Builder Class)55 mins
Application of Biotechnology48 mins
Application of Biotechnology | Concepts - 0256 mins
Application of Biotechnology Part 229 mins
Application of Biotechnology | Concepts - 0160 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses