Question

Find values of a and b such that f is differentiable everywhere.
f(x) = {2cosx if x < pi/2}
{ax - b if x > & = pi/2}

Answer 1

to be differentiable at pi/2 then it should be continuous and the lim f(x) at pi/2 should exist

2cos(pi/2) = a(pi/2)-b
0 = a(pi/2) -b
b = a(pi/2)

set the derivatives equal at pi/2
-2sin(pi/2) = a
-2 = a

--> b = -2(pi/2) = -pi