# If f(2) = 3 and f ' (2) = -1, then what is f(x)

This is more of a generic question...but it's shown up in so many of my homework questions that I thought I would consult the pros at PF.

If I am given...let's say:

f(2) = 3
f'(2)= -1

How would I go about finding f(x)

Related Calculus and Beyond Homework Help News on Phys.org
rock.freak667
Homework Helper
...integration is the reverse of differentiation...

i.e. $$\int f'(x) dx=f(x)+C$$

Knowing the value of the function and its derivative at only one point (x=2) tells you nothing about the behavior of the function anywhere else, so no, you can't find f(x) just from those two pieces of information. In other words, f could be a straight line, a parabola, an infinite polynomial series, etc.

Thanks for the fast replies!

I haven't learned integration yet.

So then how do you propose I do this question. (Actual HW question)

Given:
g(2) = 3
g'(2) = -2
h(2) = -1
h'(2) = 4

f(x) = g(x)/h(x)

Find f'(2)

rock.freak667
Homework Helper
Use the quotient rule to find f'(x) and then sub x=2.Then sub the values that you were given.

Thanks for the fast replies!

I haven't learned integration yet.

So then how do you propose I do this question. (Actual HW question)

Given:
g(2) = 3
g'(2) = -2
h(2) = -1
h'(2) = 4

f(x) = g(x)/h(x)

Find f'(2)
Try differentiating f(x). You should get a result in terms of g, g', h, and h'. Plug in and you're done. :)

Genius! Thanks :D