anonymous 4 years ago Find the function f given that it satisfies f''(x)=36x^2+24x and its graph has a horizontal tangent line at the point (0,1)

1. anonymous

Find the anti-derivative 2 times.. So first $f \prime (x) = 12x^3 + 12x^2 + C$

2. anonymous

f''(x)=3x^4+4x^3+c then what?

3. anonymous

$f(x) = 3x^4 + 4x^3 + Cx + D$

4. anonymous

Question is how do I find D?

5. anonymous

We need to find what Cx and what D is.. Im trying to think how to do that

6. anonymous

We know that F(0)=1

7. anonymous

Right which would make Cx = 1

8. anonymous

So we have $f(x) = 3x^4 + 4x^3 + x + D$

9. anonymous

I ment it would make C = 1.. not Cx

10. anonymous

if you do that you graph does not have a horizontal tangent line at (0,1) So c=1

11. anonymous

Thank you thou but I think I new how to do it.