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Question: Let f (x) = \(\frac{\pi}{2}\) If f (x) is differentiable at x = 2, (p, q) =...

Let f (x) = π2\frac{\pi}{2}

If f (x) is differentiable at x = 2, (p, q) =

A

(8, – 5)

B

(– 5/2,3)

C

(– 10, 4)

D

None of these

Answer

(8, – 5)

Explanation

Solution

Q diff. at x = 2 ⇒ conti. at x = 2

∴ f(2) = f(2+) ⇒ 6 – p = 8 + 2q ⇒ p + 2q = – 2 ....(1)

Now f '(x) = [3,0<x<24x+q,2<x≤3\left[ \begin{array} { c c c } 3 & , & 0 < x < 2 \\ 4 \mathrm { x } + \mathrm { q } & , & 2 < \mathrm { x } \leq 3 \end{array} \right.

∴ f '(2+) = f '(2–) ⇒ 8 + q = 3 ⇒ q = – 5, P = 8