Mat 270: Calc 3.10

Question

The linear approximation at x=0 to f(x)= 1/sqrt(9-x) is L(x) = A +Bx

I have to find A and B. I was able to find A by plugging in 0 to f(x). I'm having trouble finding B

Answer 1

L(x) = f(0) + f'(0)x

f(x) = (9-x)^-1/2

f'(x) = -1/2(9-x)^-3/2(-1) = 1 / [2(9-x)^3/2]

f'(0) = 1/54