Question

Find the linear approximation of 𝑓(𝑥)=√(𝑎+𝑏𝑥) at 𝑥=0 . (Here 𝑎 and 𝑏 are constants; assume 𝑎>0 .)

Answer 1

at x = 0, y = sqrt a

dy/dx = d/dx(a+bx)^.5 = .5 b / (a+bx)^.5
so at x = 0 slope m = .5 b/sqrt a
so
y = (.5 b/sqrt a) x + sqrt a