IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

nandithac

if f(x)=[mod(x)]^3 show that f"(x) exists for all real x and find it

richa_dpsvk

by [], do u mean the GIF?

nandithac

nope i mean modulus

ramkumar_november

Here is the solution......

f(x) = x³ , x>0

-x³ , x<0

find LHD and RHD at x=0

both will be equal so it is differentiable

f ' (x) = 3x² , x>0

-3x² , x<0

now for f ' (x) find LHD and RHD at x=0

both will be equal so f ' (x) is differentiable ....

f '' (x) = 6x , x>0

-6x , x<0

so f '' (x) exists for all real x and it is

f '' (x) = 6x , x>0

-6x , x<0

clear with my solution??

arpan1

see in this ques. first draw the graph

secondly f₂(x) = 6 mod(x)

it is a strictly decreasing function for x= - (infinity) to 0 and strictly increasing from 0 to infinity...

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