Home
Class 12
MATHS
Find all the points of local maxima and...

Find all the points of local maxima and minima of the function f given by `f(x)= 4x^(3)-12x^(2)+12x+10`

Text Solution

Verified by Experts

`f(x)= 4x^(3)-12x^(2)+12x+10`
`f'(x)=12x^(2)-12x+12`
`=12(x^(2)-2x+1)`
`=12(x-1)^(2)`
f'(x)=0 at x=1 but f'(x) does not change sign about x=1 , i.e., `f'(x) ge 0`, hence f(x) has neither point of maxima nor point of minima .
x=1 is point of inflection .
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise TRY YOURSELF|39 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise Assignment SECTION-A (Competition Level Questions)|50 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

Similar Questions

Explore conceptually related problems

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

Find all points of local maxima and local minima of the function f given by f(x)=x^(3)-3x+3

Find all the points of local maxima and local minima of the function f given by f(x)=2x^(3)-6x^(2)+6x+5

Find all the points of local maxima and local minima of the function f given by quad f(x)=2x^(3)-6x^(2)+6x+5

Find all the points of local maxima and local minima of the function f(x)=x^(3)-6x^(2)+12x-8

Find all the points of local maxima and local minima of the function f(x)=x^(3)-6x^(2)+12x-8

Find all the points of local maxima and minima of the function f given by f(x)= sinx- cosx , x in [0,2pi]

Find all the points of local maxima and local minima of the function f(x)=(x-1)^(3)(x+1)^(2)

Find the points of local maxima and minima of the function f(x)=x^(2)-4x .

Find all the points of local maxima and minima of the function f(x)=x^(3)-6x^(2)+9x-8