Question

Let $f(x)=\begin{cases}\tan x & \text { if } 0 \leq x \leq \frac{\pi}{4} \\ a x+b & \text { if } \frac{\pi}{4}< x< \frac{\pi}{2}\end{cases}$. If $f(x)$ is differentiable at $x=\frac{\pi}{4}$, then the values of $a$ and $b$ are respectively

• A. $2, \frac{2-\pi}{2}$
• B. $2, \frac{4-\pi}{4}$
• C. $1, \frac{-\pi}{4}$
• D. $2, \frac{-\pi}{4}$
• E. $222,1-\pi$

Answer 1

Answer: (A)

Correct answer is (a) $2, \frac{2-\pi}{2}$