How do I find the difference quotient? I already have the function of x and the equation and the restriction. How do I start?

Question

raden · Answer

share ur question, please...

anonymous · Answer

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

raden · Answer

about derivative by using limit methods, right ?

anonymous · Answer

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

anonymous · Answer

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 $-6-h$

anonymous · Answer

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

raden · Answer

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

anonymous · Answer

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

anonymous · Answer

Thank you!! both of your answers were very helpful!

anonymous · Answer

yw