## heckyeahrobin 3 years ago How do I find the difference quotient? I already have the function of x and the equation and the restriction. How do I start?

2. heckyeahrobin

i have already plugged in (3+h) for x. what do i do next? @RadEn

about derivative by using limit methods, right ?

4. satellite73

\(f(6)=5\) so we keep that number

5. satellite73

then compute \[f(6+h)=5+6(6+h)-(6+h)^2\] to get \[5+36+6h-(36+12h+h^2)\] \[=5-6h-h^2\] then subtract 5 so that \(f(6+h)-f(6)=-6h-h^2\) divide by \(h\) and get \(-6-h\)

6. heckyeahrobin

so i don't divide by H until i have plugged in both 6+h and 6 and simplified both? @satellite73

smart way : f(x) = 5+6x-x^2 f'(x) = 6-2x if u want find value of f'(6), u just plug in x=6 into f'(x) so, f'(6)=6-2(6)=6-12= ????????? but if u want using limit's method, like @satellite73 said

8. satellite73

you do not divide by \(h\) until the end one reason is that you cannot divide by \(h\) until you have simplified the numerator so that everything without an \(h\) in it is gone

9. heckyeahrobin