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

1. Jan 5, 2008

### Big-J

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)

2. Jan 5, 2008

### rock.freak667

...integration is the reverse of differentiation...

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

3. Jan 5, 2008

### belliott4488

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.

4. Jan 5, 2008

### Big-J

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)

5. Jan 5, 2008

### rock.freak667

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

6. Jan 5, 2008

### foxjwill

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

7. Jan 5, 2008

### Big-J

Genius! Thanks :D