Question

Find the linear approximation of f(x)=√4-x at a=0 and use it to approximate √3.9 and √4.1.

L(x)=
√3.9≈
√4.1≈

Answer 1

So we just need to find the tangent line to f at a=0

We need the following info
f'(x)
f'(a)
Then enter into here:
y-f(a)=f'(a)(x-a)

Answer 2

We will use that y to approximate f=sqrt(4-x)

Answer 3

so f'(x) is (1/2) (4-x)^(-1/2) * (-1) right?

Answer 4

f'(a) = (1/2)(4-a)^(-1/2) * (-1) right?

Answer 5

yep...and a=0, correct?

So f'(0)=-1/2 * (4-0)^(-1/2)