**Find the linear approximation of the function ***f*(*x*) = √(25-x) at *a* = 0 and use it to approximate the numbers √24.9 and √24.99. **L(x)=**
$\displaystyle L(x)=f(a)+f'(a)(x-a)$

$\displaystyle f'(a)=\frac{1}{2sqrt(25-x)}$

***
$\displaystyle f'(0)=\frac{1}{10}$

$\displaystyle f(a)=5$

$\displaystyle

L(x)=5 +\frac{1}{10}(x-25)$

(I used this to get the **√24.9 and √24.99; (4.99, 4.999 respectively)**,

**but...**

$\displaystyle

L(x)=\frac{50}{10} + \frac{1}{10}x - \frac{25}{10}$

$\displaystyle L(x)=$

**I put this in for part a, and it was marked wrong. A=0, but if I put (x-0) instead of (x-25) it becomes a number greater than 5, which won't make sense considering you plug in a number lower than 25.**