Home
Class 12
MATHS
If S(1) and S(2) are respectively the se...

If `S_(1) and S_(2)` are respectively the sets of local minimum and local minimum and local maixmum pointof the functio, `f(x)=9x^(4)+12x^(2)-36x^(2)+25, x in R`, then

A

`S_1={-2},S_2={0,1}`

B

`S_1={-2,1},S_2={0,1}`

C

`S_(1)={-1},S_2={0,2}`

D

`S_1={-2,0} ,S_2={1}`

Text Solution

Verified by Experts

The correct Answer is:
B
`f'(x)=36x^3+36x^2-72x`
`=36(x^3+x^2-2x)`
`=36x(x^2+x-2)`
`=36x(x+2)(x-1)`
Sign scheme of f'(x)is
Local minimum at –2 and 1
Local maximum at 0
`S_1={-2,1},S_2={0}`
Promotional Banner

Similar Questions

Explore conceptually related problems

If S_(1) and S_(2) are respectively the sets of local minimum and local maximum point of the function, f(x)=9x^(4)+12x^(3)-36x^(2)+25, x in R , then (a) S_(1)={-2}:S_(2)={0,1} (b) S_(1)={-2,0}:S_(2)={1} (c) S_(1)={-2,1}:S_(2)={0} (d) S_(1)={-1}:S_(2)={0,2}

Find the points of maximum ( local maximum ) and minimum ( local minimum ) of the function f(x)=x^(3)-3x^(2)-9x ?

Find local maximum and local minimum values of the function f given by f(x)=3x^(4)+4x^(3)-12x^(2)+12

Find the points of local maxima and local minima of the function f(x)=2x^(3)-3x^(2)-12x+8 .

Find the local maxima and minima of the function f(x)=2x^(3)-21x^(2)+36x-20 .

The point (s) of local maxima and local minima of the funcation f(x) = 3x^(4) -8x^(3) +12 x^(2)-48 x +1 are :

Find the points of local maxima and local minima,if any,and local maximum and local minimum values of f(x)=s in^(4)x+cos^(4)x

Find the local maximum and local minimum value of f(x)= x^(3)-3x^(2)-24x+5

Find the points of local maxima and minima of the function f given by f(x)= x^(3)-12x^(2)+36x+5 .

Find the sum of the local maximum and local minimum values of the function f (x) = (tan 3x)/(tan^(3) x) on interval (0 , pi//2) .