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

If the function f given by
f(x)=x33(a2)x2+3ax+7, for some aR is increasing in (0,1] and decreasing in [1,5), then a root of the equation,
f(x)14(x1)2=0 (x1) is :

A
7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
7
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 7
f(x)=x33(a2)x2+3ax+7
f(x)=3x26(a2)x+3a
f(x)0 x(0,1]
f(x)0 x[1,5)
x=1 is a critical point.
f(1)=0
36a+12+3a=0
​​​​​​​a=5
​​​​​​​
​​​​​​​f(x)14(x1)2=0
​​​​​​​x39x2+15x7(x1)2=0
(x1)2(x7)(x1)2=0
​​​​​​​x=7 is a root.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Extrema
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon