# Function and its tangent

1. Jan 26, 2010

### flyers

1. The problem statement, all variables and given/known data

Find the equation f(x) who's integral is $$\int x^{3}$$ and has a tangent x+y=0

2. Relevant equations

3. The attempt at a solution

I know that f(x) is 1/4x4+c because of the integral. The tangent is the derivative of f(x) at some point

i have the equations

y=x3+c
y=-x

but solving these equations gives me two unknowns...

2. Jan 26, 2010

### Char. Limit

Well, at what point does x^3 equal negative 1 (the slope of y=-x)

3. Jan 26, 2010

### Staff: Mentor

What you have written is not very clear. From what I can tell, f(x) = (1/4)x4 + C.

You're given that f is tangent to the graph y = -x. This means that f'(x) = x3 has to equal -1 (the slope of the line y = -x). It also means that the graph of f has to have a point in common with the line y = -x.

4. Jan 26, 2010

### flyers

-1?
so

1/4x4+c=1
1/4(-1)+c=1
c=3/4

f(x)= 1/4x4+3/4

5. Jan 26, 2010

### Staff: Mentor

-1 for what?
Why 1? You're not explaining what you're doing, which makes it extremely difficult to understand your work.

6. Jan 26, 2010

### flyers

Sorry, I was replying to Char. limit's question

7. Jan 27, 2010

### Staff: Mentor

Can you post the problem exactly as it is worded? I'm having a hard time believing this is what you have actually been given:
especially the part that says "who's integral is $\int x^{3}$..."