Approximating Square Roots with Linear Approximation

[thushanthan]

Homework Statement

Given f(x)=sqrt(2x+2)

Question : Find the linear approximation of f(x) at a=7 AND use it to approximate sqrt(18).

Homework Equations

L(x)=f(a)+f'(a)(x-a)

The Attempt at a Solution

Using the linear approximation formula I am getting the value 6.75, but when I checked with calculator the value of sqrt(18) is 4.2426...

Did my approximation is wrong?

 

[D H]

Yes, you did something wrong. Show us your work. It's kinda hard to tell where you went wrong without that.

 

[thushanthan]

Thank you

I didn't solve 2x+2=18. I plugged in x=18 and (x-a) becomes (18-7) = 11.

Now I got it. Thanks.