Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If f (x) = 3x 4 + 4x 3 – 12x 2 + 12, then f(x) is
A
increasing in (- 
, - 2) 
(0, 1)
, - 2) (0, 1)
B
increasing in (-2, 0) 
(1, 
)
(1, )
C
decreasing in (-2,0) 
(0,1)
(0,1)
D
decreasing in(- 
,-2) 
(1, 
)
,-2) (1, )
Text Solution
Verified by ExpertsThe correct answer is:
B
increasing in (-2, 0) 
(1, 
)
Since, f(x) = 3x 4 + 4x 3 - 12x 2 + 12
f' (x) = 12x 3 + 12x 2 - 24x
= 12x(x-1)(x+ 2)
The above expression it is clear that f(x) is increasing in (-2, 0) 
(1, 
) and decreasing in (- 
, - 2) 
(0, 1)
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The volume of a cube is increasing at the rate of 18 cm 3 per second. When the edge of the cube is …
If f (x) = cos |x|- 2ax + b is a function which increases for all x, then the maximum value of 2a +…
Let y = x 3 - 6x 2 + 9x + 1 be an equation of a curve, then the x -intercept of the tangent to this…
If is the only real root of x 3 + bx 2 + cx + 1 = 0 (b< c), then the value of | [ ] | is (where, …
Let y = x 3 -6x 2 + 9x + 1 be the equation of a curve, then the x -intercept of the tangent to this…
The number of point(s) on the curve y 3 = 12y - 3x 2 where a tangent is vertical is/are