Home
Class 12
MATHS
Find local minimum value of the function...

Find local minimum value of the function f given by `f(x)=3+|x|,x in R`.

Text Solution

Verified by Experts

f(x)=3+|x|
=3-x,when x<0
=3, when x=0
=3+x, when x>0
x<0 `->` f'(x)=-1 decreasing
x>0 `->` f'(x)=+1 increasing
x=0 `->` f'(x)=0
there for, f(0)=3 is the local minima
Promotional Banner

Similar Questions

Explore conceptually related problems

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

Find the maximum and the minimum values, if any, of the function f given by f(x)=x^2,x in R .

Find the maximum and minimum values of any of the function f given by f(x)=x^(4) , x in R .

Find the maximum and minimum values of f , if any, of the function given by f(x)=|x|,x in R .

Find the maximum and minimum value if any , of the function f given by f(x)=5-|x-1| .

Find the absolute maximum and minimum values of the function f given by f(x)=cos^2x+sinx , x in [0,\ pi] .

Find the absolute maximum and minimum values of the function f given by f(x)=cos^2x+sinx , x in [0,pi]

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

Find the maximum and the minimum values, if any, of the function given by f(x)=x ,x in (0,1)

Find the maximum and minimum values , if any , of the function f given by f(x)=3-|x|