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

If f(x)=x2{2(t2)(t3)3+3(t2)2(t3)2} dt, then which of the following is/are correct?

A
x=2 is point of local maximum
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x=3 is point of local minimum
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x=125 is point of local minimum
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x=3 is point of inflection
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct options are
A x=2 is point of local maximum
C x=125 is point of local minimum
D x=3 is point of inflection
f(x)=2(x2)(x3)3+3(x2)2(x3)2
=(x2)(x3)2[2(x3)+3(x2)]
=(x2)(x3)2[5x12]
For f(x)=0, we get
x=2, x=3 and x=125

f′′(x)=(x3)2(5x12) +2(x2)(5x12)(x3) +5(x2)(x3)2
f′′(2)=2<0
x=2 is local maximum.
f′′(3)=0 and f′′′(3)0
x=3 is point of inflection.
f′′(12/5)=525925>0
x=125 is point of local minimum.

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