2007-09-25 08:57:51 · 4 answers · asked by william5000forever 2 in Science & Mathematics ➔ Mathematics
f(x) = 5x^2 + 7x
f(x+h) = 5(x+h)^2 +7(x+h) = 5x^2 + 10xh + 5h^2 + 7x + 7h
f(x+h) - f(x) = 10xh + 5h^2 + 7h
[f(x+h) - f(x)] / h = (10xh + 5h^2 + 7h) / h
= 10x + 5h + 7
2007-09-29 19:49:10 · answer #1 · answered by MsMath 7 · 0⤊ 3⤋
replace: f(3 + h) = 2(3 + h)^2 - (3 + h) = 2(9 + 6h + h^2) - (3 + h) = 18 + 12h + 2h^2 - 3 - h = 15 + 11h + 2h^2 And f(3) = 2(3)^2 - 3 = 18 - 3 = 15 the numerator will become 15 + 11h + 2h^2 - 15 = 11h + 2h^2 component the h interior the numerator to get (h(11 + 2h))/h = 11 + 2h
2016-12-28 03:07:11 · answer #2 · answered by ? 3 · 0⤊ 0⤋
f `(x) = lim h->0 [ f(x + h) - f(x) ] / h h ≠ 0
Numerator, N
5(x + h) ² - 5x² + 7(x + h) - 7x
5 x ² + 10 h x + 5 h ² - 5 x ² + 7 x + 7 h - 7 x
10 h x + 5 h ² + 7 h
Denominator, D
h
N/D = 10 x + 5 h + 7
N/D = 10 x + 7 as h->0
f `(x) = 10 x + 7
2007-10-01 21:00:52 · answer #3 · answered by Como 7 · 2⤊ 1⤋
Something tells me you're trying to take the derivative.
The derivative is 10x + 7.
2007-09-25 09:21:07 · answer #4 · answered by PMP 5 · 2⤊ 1⤋