If a function y = f(x) is diffrentiable at x = 3 and f '(3) = 5, and find the limit
lim ((x^(2)-3x))/(f(3)-f(x))
x goes to 3

Question

If a function y = f(x) is diffrentiable at x = 3 and         f '(3) = 5, and find  the limit
lim          ((x^(2)-3x))/(f(3)-f(x))
x goes to 3

kainui · Answer

If you try to plug in a 3 you find that you get 0/0 which is an indeterminate form. So you can use L'hopital's rule which says that the derivative of the top divided by the derivative of the bottom is equal to the limit.

anonymous · Answer

thank you for your response. It seems if I use that method, then the information given in the question where f prime 3 is equal to 5 is not useful

anonymous · Answer

do you think Lhopital rule is the only method for this question?

anonymous · Answer

thank you for the graph. I fully understand what you mean

kainui · Answer

Actually I don't know, maybe.

kainui · Answer

But by L'hopital's rule I got the limit as x->3 to be infinity.

zarkon · Answer

$$\frac{d}{dx}f(3)=0$$

anonymous · Answer

yep I got infinity as well
I got zero for the denominator

kainui · Answer

d/dx(f(3))=5 Zarkon

zarkon · Answer

$$\frac{d}{dx}[f(3)-f(x)]=-f'(x)$$

kainui · Answer

Reread the problem, it's stated.

zarkon · Answer

no...$$\left.\frac{d}{dx}f(x)\right|_{3}=5$$

zarkon · Answer

f(3) is just a number
the derivative of a number is zero

anonymous · Answer

did you get 3/-5 as the answer Zarkon?

zarkon · Answer

yes

kainui · Answer

"y = f(x) is diffrentiable at x = 3 and         f '(3) = 5"

kainui · Answer

f'(3)=d/dx(f(3))

zarkon · Answer

that is incorrect

kainui · Answer

Yeah, I you're right.

anonymous · Answer

((x^(2)-3x))/(f(3)-f(x))= -x/ ((f(x)-f(3))/(x-3))
lim (f(x)-f(3))/(x-3) x goes to 3 = f'(3)=5
so the answer is -3/5