Home
Class 12
PHYSICS
The maximum and minimum values of x^3-18...

The maximum and minimum values of `x^3-18x^2+96x` in interval `(0,9)` are

A

160,0

B

128,160

C

160,128

D

0,160

Text Solution

Verified by Experts

The correct Answer is:
C
Let `y=x^(3)-18x^(2)+96ximplies(dy)/(dx)=3x^(2)-36x+96=0`
`becausex^(2)-12x+32=0implies(x-4)(x-8)=0,x=4,8`
Now `(d^(2)Y)/(dx^(2))=6x-36`
At `x=4(d^(2)y)/(dx^(2))=24-36=-12lt0`
At `x=4` function will be maximum
And `[f(4)]_(max)=64-288+384=160`
At `x=8,(d^(2)y)/(dx^(2))=48-36=12gt0`
At `x=8`, function will be minimum and `[f(8)]_(min)=128`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the maximum and minimum values of f(x)=x+sin2x in the interval [0,\ 2pi]

Find the maximum and minimum values of f(x)=2x^3-24 x+107 in the interval [1,\ 3] .

Find the maximum and minimum values of f(x)=x^(50)-x^(20) in the interval [0,1] .

Find the maximum and minimum values of f(x)=x^(50)-x^(20) in the interval [0,\ 1] .

The maximum & minimum value of y=x+(1)/(x) in interval [(1)/(3),(4)/(3)]

Find both the maximum and the minimum value of 3x^4-8x^3+ 12 x^2-48 x+1 on the interval [1,4] .

Find both the maximum and the minimum value of 3x^4-8x^3+ 12 x^2-48 x+1 on the interval [1,4] .

A curve y=f(x) satisfies (d^2y)/dx^2=6x-4 and f(x) has local minimum value 5 at x=1 . If a and b be the global maximum and global minimum values of f(x) in interval [0,2] , then ab is equal to…

The minimum value of 9^x+9^(1-x),x inR, is

Find the maximum and the minimum values of f(x)=3x^2+6x+8,\ \ x in R , if any.