GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 33 of 65

Marks: +1, -0

Let be a real-valued function of a real variable defined as

f(x)=x^2

for

x ≥ 0

,and

f(x)=-x^2

for

x < 0

Which one of the following statements is true?

$f(x)$ is discontinuous at $x=0$
$f(x)$ is discontinuous at $x=0$
$f(x)$ is differentiable but its first derivative is not continuous at $x=0$ .
$f(x)$ is differentiable but its first derivative is not differentiable at $x=0$ .

Solution:

f^{'}(x)=\{\table x^2 , x ≥ 0 ; - x^2 , x<0.

f^{'}(x)=\{\table 2 x , x ≥ 0 ; -2 x , x<0.

f(x)=\{\table 2 , x ≥ 0 ; -2 , x<0.

The first derivation of

f(

i.e

) f^{'}(x)

is not derivable at

x=0

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