If f(x) = cases 1/|x|, & x ≥ 1 \\ ax^2+b, & x < 1 cases is differentiable at x=1 then Option 1: a=1/2, b=-3/2 Option 2: a=-1/2, b=3/2 Option 3: a=-1/2, b=-3/2 Option 4: a=1/2, b=3/2

The answer is 'a=-1/2, b=3/2'. View full solution:

CUET Mathematics - If f(x) = cases 1/|x|, & x ≥ 1 \\ ax^2+b, & x < 1 cases is differentiable at x=1 then | PYQs + Solutions

CUET Mathematics 2026 15th May Shift 1

Calculus

Medium

core

$a=\dfrac{1}{2}, b=-\dfrac{3}{2}$

$a=-\dfrac{1}{2}, b=\dfrac{3}{2}$

$a=-\dfrac{1}{2}, b=-\dfrac{3}{2}$

$a=\dfrac{1}{2}, b=\dfrac{3}{2}$

✅ Correct Option: 2