Question

please help, stuck on this problem. find difference of f, f(x+h)-f(x) over h f(x)=5x^2-9x+8

Answer 1

f '(x)=10x-9

Answer 2

I think the purpose is to evaluate the limit of the difference quotient instead of simply differentiating.

Answer 3

\[\frac{5x^{2}+10xh+5h^{2}-9x-9h+8-5x^{2}+9x-8}{h}=\frac{10xh+5h^{2}-9h}{h}=10x-9\]

Answer 4

when you take the limit in the last step of course.

Answer 5

To clarify what he did:
\[\lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}{h}\]

Answer 6

should it be 10x-9h? or just 10x-9?

Answer 7

the limit is the derivative, 10x-9

Answer 8

thank you both for your help! much appreciated