giggles123
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)



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Tyler1992
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Find the antiderivative 2 times.. So first \[f \prime (x) = 12x^3 + 12x^2 + C\]

giggles123
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f''(x)=3x^4+4x^3+c then what?

Tyler1992
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\[f(x) = 3x^4 + 4x^3 + Cx + D\]

giggles123
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Question is how do I find D?

Tyler1992
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We need to find what Cx and what D is.. Im trying to think how to do that

giggles123
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We know that F(0)=1

Tyler1992
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Right which would make Cx = 1

Tyler1992
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So we have \[f(x) = 3x^4 + 4x^3 + x + D\]

Tyler1992
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I ment it would make C = 1.. not Cx

giggles123
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if you do that you graph does not have a horizontal tangent line at (0,1)
So c=1

giggles123
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Thank you thou but I think I new how to do it.