Home
Class 12
MATHS
If f(x)=max{x^(2)-4,|x-2|,|x-4|} then:...

If `f(x)=max{x^(2)-4,|x-2|,|x-4|}` then:

A

f (x) is continuous for all ` x in R`

B

f (x) is differentiable except at `x=(-1 pm sqrt33)/(2)`

C

f (x) has a critical point at x =2

D

f (x) has no maximum

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)=max*{|x^(2)-2|x||,|x|} then number of points where f(x) is non derivable, is :

Discuss the differentiability of f(x)=max{x^(2)-3x+2,2-|x-1|}

For each real x, let f(x)=max{x,x^(2),x^(3),x^(4)} then f(x) is

Sometimes functions are defined like f(x)=max{sinx,cosx} , then f(x) is splitted like f(x)={{:(cosx, x in (0,(pi)/(4)]),(sinx, x in ((pi)/(4),(pi)/(2)]):} etc. If f(x)=max{x^(2),2^(x)} ,then if x in (0,1) , f(x)=

Find the equivalent definition of f(x)=max{x^(2),(1-x)^(2),2x(1-x)} where 0<=x<=1

Let f(x)=max.{|x^(^^)2-2|x||,|x|} and g(x)=min.{|x^(^^)2-2|x||,|x|} then

If f(x)=max{x^(2),(1-x)^(2),(3)/(4)},x in[0,1] then the value of of int_(0)^(1)f(x)dx is

Sometimes functions are defined like f(x)=max{sinx,cosx} , then f(x) is splitted like f(x)={{:(cosx, x in (0,(pi)/(4)]),(sinx, x in ((pi)/(4),(pi)/(2)]):} etc. If f(x)=max{(1)/(2),sinx} , then f(x)=(1)/(2) is defined when x in

f(x)=max{tan x,cot x)