Question

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)

Answer 1

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

Answer 2

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

Answer 3

\[f(x) = 3x^4 + 4x^3 + Cx + D\]

Answer 4

Question is how do I find D?

Answer 5

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

Answer 6

We know that F(0)=1

Answer 7

Right which would make Cx = 1

Answer 8

So we have \[f(x) = 3x^4 + 4x^3 + x + D\]

Answer 9

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

Answer 10

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

Answer 11

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