Let f(x)= begincases tan x text if 0 ≤ x ≤ (π/4) a x+b text if (π/4)

Question

Let f(x)= begincases tan x text if 0 ≤ x ≤ (π/4) a x+b text if (π/4)< x< (π/2) endcases. If f(x) is differentiable at x=(π/4), then the values of a and b are respectively (A) 2, (2-π/2) (B) 2, (4-π/4) (C) 1, (-π/4) (D) 2, (-π/4)

Tardigrade Admin · Accepted Answer

Correct answer is (a) 2, (2-π/2)

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

$2, \frac{2 - π}{2}$

$2, \frac{4 - π}{4}$

$1, \frac{- π}{4}$

$2, \frac{- π}{4}$

$222, 1 - π$

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

Q. Let f(x)={tanxax+b​ if 0≤x≤4π​ if 4π​<x<2π​​. If f(x) is differentiable at x=4π​, then the values of a and b are respectively

2,22−π​

2,44−π​

1,4−π​

2,4−π​

222,1−π

Correct answer is (a) 2,22−π​