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giggles123

  • 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)

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  1. Tyler1992
    • 4 years ago
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    Find the anti-derivative 2 times.. So first \[f \prime (x) = 12x^3 + 12x^2 + C\]

  2. giggles123
    • 4 years ago
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    f''(x)=3x^4+4x^3+c then what?

  3. Tyler1992
    • 4 years ago
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    \[f(x) = 3x^4 + 4x^3 + Cx + D\]

  4. giggles123
    • 4 years ago
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    Question is how do I find D?

  5. Tyler1992
    • 4 years ago
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    We need to find what Cx and what D is.. Im trying to think how to do that

  6. giggles123
    • 4 years ago
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    We know that F(0)=1

  7. Tyler1992
    • 4 years ago
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    Right which would make Cx = 1

  8. Tyler1992
    • 4 years ago
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    So we have \[f(x) = 3x^4 + 4x^3 + x + D\]

  9. Tyler1992
    • 4 years ago
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    I ment it would make C = 1.. not Cx

  10. giggles123
    • 4 years ago
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    if you do that you graph does not have a horizontal tangent line at (0,1) So c=1

  11. giggles123
    • 4 years ago
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    Thank you thou but I think I new how to do it.

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