Question

If f(x) = $\left\{ \begin{matrix} \tan^{- 1}x & if|x| \leq 1 \\ \frac{1}{2}\left( |x| - 1 \right) & if|x| > 1 \end{matrix} \right.\$is differentiable ∀ x , then value of a and b is-

• A. a = 1/2, b = –3/2
• B. a = –1/2, b = 3/2
• C. a = 3/2, b= ½
• D. None of these

Answer 1

Answer: (B)

a = –1/2, b = 3/2

Answer 2

f(x) = f(x) = $\left\{ \begin{array} { c c } - \frac { 1 } { x } & x \leq - 1 \\ a x ^ { 4 } + b & - 1 < x < 1 \\ \frac { 1 } { x } & x > 1 \end{array} \right.$

at x = 1 continuous a.1 + b = 1 …(1)

at x = 1 differentiable 2ax = –

at x = 1 2a = –1

a = –1/2 using (1) b = 3/2