anonymous
  • anonymous
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)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Find the anti-derivative 2 times.. So first \[f \prime (x) = 12x^3 + 12x^2 + C\]
anonymous
  • anonymous
f''(x)=3x^4+4x^3+c then what?
anonymous
  • anonymous
\[f(x) = 3x^4 + 4x^3 + Cx + D\]

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anonymous
  • anonymous
Question is how do I find D?
anonymous
  • anonymous
We need to find what Cx and what D is.. Im trying to think how to do that
anonymous
  • anonymous
We know that F(0)=1
anonymous
  • anonymous
Right which would make Cx = 1
anonymous
  • anonymous
So we have \[f(x) = 3x^4 + 4x^3 + x + D\]
anonymous
  • anonymous
I ment it would make C = 1.. not Cx
anonymous
  • anonymous
if you do that you graph does not have a horizontal tangent line at (0,1) So c=1
anonymous
  • anonymous
Thank you thou but I think I new how to do it.

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