wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If f(x)=x3+4x2+kx+1 is a monotonically decreasing function of x in the largest possible interval (-2, -2/3). Then .

A
k = 4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
k = 2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
k = -1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
k has no real value
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A k = 4
Here,f'(x)0or, 3x2+8x+k0, x(2, 23)
Since, 3x2+8x+k represents a upward parabola. Then , the situation for f '(x) are as follows:
Case1.

Case2.

Given that f(x) decreases in the largest possible interval (2,23). Then,f '(x) must have roots -2 and -2/3.
Thus, Product of roots= (2) (23) =k3or, k=4.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Monotonicity
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon