CBSE Class 12 Math 2023 All Sets Solved Paper

Question : 11 of 20

Marks: +1, -0

The function f(x) = x | x | is:

Solution:

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

x=0

\lim ↙{x → 0^{-}}-x^2=0 \text " and " \lim ↙{x → 0^{+}} x^2=0

\lim ↙{x → 0^{-}} f(x)=\lim ↙{x → 0^{+}} f(x)=f(0)

∴ \text "f"(\text "x")

is continuous at

\text "x"=0

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

x=0

\;{d}/{d x} f(x) {{}/{} |}_{0^{-}}=\;{d}/{d x} f(x) {{}/{} |}_{0^{+}}=0

∴ \text "f"(\text "x")

is differentiable at

\text "x"=0

Go to Question:

Prev Question

Next Question