## april1renee 2 years ago f(x)=5x^2 f(x+h)-f(x)/h

f(x+h) means where you see the x you add h DO NOT FOCUS ON OTHER NUMBERS

2. Zelda

10x Should be the final answer.

@Zelda theres no limit here

4. april1renee

5(x+h)^2 -f(5x^2) ??

yes then divide by h

6. april1renee

5(x^2+2xh+h^2)= 5x^2+10xh+5h^2

7. april1renee

5x^2+10x+5h

8. Zelda

Hey april, is there the word lim as h-> 0 before f(x)?

5x^2+10xh+5h^2-(5x^2+10x+5h)=

10. april1renee

the answer i have is 10x+5h

yes but is there any thing like this $\lim_{h \rightarrow 0}$ on the question

12. april1renee

no

13. april1renee

professor answer is 5(2x+h) i dont undestand why i would divide by 5

14. ZeHanz

It would be (very much) more clear if everyone wouldn't just write peaces of the problem, but the whole thing:$\frac{ f(x+h)-f(x) }{ h }=\frac{ 5(x+h)^2-5x^2 }{ h }=\frac{ 5(x^2+2xh+h^2)-5x^2 }{ h }$See? Just keep on writing the complete fraction, simpifying it along the way, until you're done:$\frac{ 5x^2+10xh+5h^2-5x^2 }{ h }=\frac{ 10xh+5h^2 }{ h }=\frac{ 5h(2x+h) }{ h }=5(2x+h)$So finally we've lost the fraction! Sooner or later the question of what will happen if h goes to 0 will be asked. Here you see immediately that leads to 10x.

15. ZeHanz

Of course, you could write the answer also as 10x + 5h

16. april1renee

THANK YOU!

17. ZeHanz

You're welcome!