Question

Using linear approximation to solve sqrt 49.4
as follows; let ƒ(x)= √x
Equation of line is @ 49 can be written as y=mx+b

where m is ? and b ?

I found m which is 0.0714286*x+7-0.0714286*49

By doing this;

ƒ'(x)=1/(2√x)

ƒ'(49)=1/2√49 =

a) L(x)= 7 + (1/14) x (x-49)
L(49.4)=7 + (1/14) x (49.4-49)

then I'm stuck at finding b

What I did was take the sqrt of 49.4, which is 7.02851335632223 but the answer says error...

Any help?

Answer 1

Slope m = f'(49) = 1/14
=> y = 1/14 ( x - 49) + 7
= x/14 + 7/2
Thus :
y = 49.4/14 + 7/2 = 7.02857

Answer 2

y = 7.02857142857

Answer 3

Thanks Chlorophyll