If f(x) = 5x² + 2x - 5, then
[f(x + h) - f(x)]/h =
2007-05-06 10:55:07 · 5 answers · asked by kat 3 in Science & Mathematics ➔ Mathematics
what is the value for h???? or are you meant to find the answer in terms of h?
2007-05-06 10:59:27 · answer #1 · answered by cookies_rule_91 3 · 0⤊ 0⤋
If f(x) = 5x^2 + 2x - 5, then
[f(x+h) - f(x)] / h
= [5(x + h)^2 + 2 (x + h) - 5 - ( 5x^2 + 2x - 5)] / h
= [5x^2 + 10xh + 5h^2 + 2x + 2h - 5 - 5x^2 - 2x + 5] / h
= [ 10xh + 5h^2 + 2h ] / h
= 10x + 5h + 2
2007-05-06 18:06:00 · answer #2 · answered by mathjoe 3 · 0⤊ 0⤋
Just plug in (x+h) to get f(x+h), subtract f(x), and put it all over h:
(f(x + h) - f(x)) / h =
([5(x + h)^2 + 2(x+h) - 5] - [5x^2 + 2x - 5]) / h
Now go ahead and simplify this. You should end up with
10x + 5h + 2
2007-05-06 18:03:59 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Hello,
f(x+h) = f(x) with x replaced by (x+h), so we have
5(x+h)^2 + 2(x+h) -5 = 5(x^2+2xh+h^2)+2x+2h-5=
5x^2+10xh+5h^2+2x+2h-5
Now f(x+h) - f(x) = 5x^2+10xh+5h^2 +2x+2h-5-(5x^2+2x-5)=
5x^2+10xh+5h^2+2x+2h-5-5x^2-2x+5= 10xh+5h^2+2h
Now divide by h and we have 10x+5h+2.
Now to find the derivative we let h approach zero and we have.
10x+2
Hope this helps.
2007-05-06 18:21:55 · answer #4 · answered by CipherMan 5 · 0⤊ 0⤋
[f(x+h)-f(x)]/h =
{ [5(x+h)² + 2(x+h) -5 ] - (5x² + 2x - 5) }/h=
[(5x²+10xh + 5h² +2x+2h+5)- (5x²+2x-5)]/h=
(10xh+5h²+2h+10)/h=
10x+5h+2+ 10/h
2007-05-06 18:04:38 · answer #5 · answered by Bladvak 3 · 0⤊ 0⤋