Let f(x) = {(1/|x| for |x| ≥ 1)(ax^2 + b for |x| < 1), If f(x) is continuous and differentiable at any point,

Question

Let \(f(x) = \begin{cases} \frac{1}{|x|} & \text{for |x|} \geq 1\\ ax^2+b & \text{for |x|} < 1 \end{cases},\) If f(x) is continuous and differentiable at any point, then

A. \(a=\frac{1}{2}, b=-\frac{3}{2}\)

B. \(a=\frac{1}{2}, b=\frac{3}{2}\)

C. a = 1, b = –1

D. None of these

Answer 1

Correct answer is D.

∵ f(x) is continuous and differentiable at any point, consider x = 1.

Putting above value in a + b = 0,

\(b = \frac{3}{2}\)