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

Find the minimum and maximum value of the function y=x33x2+6. Find the values of y at which it occurs.


A

Maxima at x = 0, Maximum value = 6

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

Maxima at x = 2, Maximum value = 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

Minima at x=0,minimum value = 6

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

Minima at x=2,minimum value = 6

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

Minima at x=2,minimum value = 6


Given y=x33x2+6
Differentiating y w.r.t. 'x', dydx=3x26x
Putting dydx=0, we will get the values at which function is maximum or minimum
3x26x=0x(3x6)=0
x=0,+2
To distinguish values of x as the point of maximum or minimum, we need 2nd derivative of the function.
d2ydx2=6x6; Now(d2ydx2)x=0=6<0
At x=0It is maximum(d2ydx2)x=2=6(2)6=6>0At x=2It is minimum
Hence x=0 is a point of maximum and x = 2 is a point of minimumSo, maximum value of y = 033.0+6=6minimum value of y=(2)33(2)2+6=2


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