SOLUTION: If f(x)= x^2 + 5, find f(a + h) - f(a). I haved tried to work this problem and the answer I got was 2ah + h^2 + 10, but it is not correct.

Algebra ->  Linear-equations -> SOLUTION: If f(x)= x^2 + 5, find f(a + h) - f(a). I haved tried to work this problem and the answer I got was 2ah + h^2 + 10, but it is not correct.      Log On


   

Question 60365This question is from textbook
: If f(x)= x^2 + 5, find f(a + h) - f(a).
I haved tried to work this problem and the answer I got was 2ah + h^2 + 10, but it is not correct. This question is from textbook

Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
If f%28x%29=+x%5E2+%2B+5
f%28a%29=a%5E2+%2B+5
f%28a+%2B+h%29+=%28a+%2B+h%29%5E2+%2B+5+=+a%5E2+%2B+2ah+%2Bh%5E2+%2B+5
f%28a+%2B+h%29+-+f%28a%29
= a%5E2+%2B+2ah+%2Bh%5E2+%2B+5+-+%28a%5E2+%2B+5%29 Need to multiply the minus sign by each term in the bracket)
= a%5E2+%2B+2ah+%2Bh%5E2+%2B+5+-+a%5E2+-+5
= 2ah+%2Bh%5E2
Note If this part of introductory calculus and the h is very, very small then h^2 would be insignificant and f(a + h) - f(a) would approximate to 2ah.)