Let f(x)={1∣x∣,∣x∣≥1ax2+b,∣x∣<1f(x) = \begin{cases} \frac{1}{|x|}, & |x| \ge 1 \\ ax^2 + b, & |x| < 1 \end{cases}…

Mathematics

Problem

Let f(x)={1∣x∣,∣x∣≥1ax2+b,∣x∣<1f(x) = \begin{cases} \frac{1}{|x|}, & |x| \ge 1 \\ ax^2 + b, & |x| < 1 \end{cases} be continuous and differentiable everywhere. Then a and b are - (A) −12,32-\frac{1}{2}, \frac{3}{2} (B) 12,−32\frac{1}{2}, -\frac{3}{2} (C) 12,32\frac{1}{2}, \frac{3}{2} (D) 32,32\frac{3}{2}, \frac{3}{2}

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