Q. 5

# Find the intervals in which the function f given by f (x) = 2x3 – 3x2 – 36x + 7 is(a) strictly increasing (b) strictly decreasing

(a) It is given that function f(x) = 2x3 – 3x2 – 36x + 7

f’(x) = 6x2 – 6x + 36

f’(x) = 6(x2 – x + 6)

f’(x) = 6(x + 2)(x – 3)

If f’(x) = 0, then we get,

x = -2, 3

So, the points x = -2 and x = 3 divides the real line into two disjoint intervals, (-∞,2), (-2,3) and (3,∞)

So, in interval

f’(x) = 6(x + 2)(x – 3) >0

Therefore, the given function (f) is strictly increasing in interval .

(b) It is given that function f(x) = 2x3 – 3x2 – 36x + 7

f’(x) = 6x2 – 6x + 36

f’(x) = 6(x2 – x + 6)

f’(x) = 6(x + 2)(x – 3)

If f’(x) = 0, then we get,

x = -2, 3

So, the points x = -2 and x = 3 divides the real line into two disjoint intervals, (-∞,2), (-2,3) and (3,∞)

So, in interval

f’(x) = 6(x + 2)(x – 3) < 0

Therefore, the given function (f) is strictly decreasing in interval.

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)FREE Class
Interactive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minima48 mins
Tangents & Normals (Concept Builder Class)FREE Class
Application of Biotechnology48 mins
Application of Biotechnology | Concepts - 02FREE Class
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