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anonymous

  • 5 years ago

Let f(x0=x^3+Ax^2+Bx-15 be a function whose graph has a maximum at x=2 and a point of inflection at x=3. Find the values of A and B?

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  1. anonymous
    • 5 years ago
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    What is f'(x)?

  2. anonymous
    • 5 years ago
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    \[f(x)=x^3+Ax^2+Bx-15\]

  3. anonymous
    • 5 years ago
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    sorry i miss read that.

  4. anonymous
    • 5 years ago
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    Now find f'(x).

  5. anonymous
    • 5 years ago
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    f'(x)=\[3x^2+2Ax+B\]

  6. anonymous
    • 5 years ago
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    and then f''(x)

  7. anonymous
    • 5 years ago
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    \[f"(x)=6x+2A\]

  8. anonymous
    • 5 years ago
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    OKay so how do we find the maxima of a polynomial?

  9. anonymous
    • 5 years ago
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    Am I suppose to plug something in?

  10. anonymous
    • 5 years ago
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    yes that's right :)

  11. anonymous
    • 5 years ago
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    So I plug the two into the original function right? Then plug the 3 into the second derivative?

  12. anonymous
    • 5 years ago
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    Do you know what is inflection point and critical points?

  13. anonymous
    • 5 years ago
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    Critical values are the zeros of the 1st dervivative and inflection points are the zeros of the 2nd derivative?

  14. anonymous
    • 5 years ago
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    Yes for the first but for the second that is only necessary condition but not sufficient condition.

  15. anonymous
    • 5 years ago
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    One also needs the lowest-order non-zero derivative to be of odd order (third, fifth, etc.). If the lowest-order non-zero derivative is of even order, the point is not a point of inflection.

  16. anonymous
    • 5 years ago
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    So what do I need to do? I'm confused now

  17. anonymous
    • 5 years ago
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    If I haven't made any error then \( A=-9 \) and you can find B accordingly :)

  18. anonymous
    • 5 years ago
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    Ignore my second last comment if it confuses you. Plug in x=3 in f''(x)=0 and then x=2 in f'(x)=0

  19. anonymous
    • 5 years ago
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    aha! I understand thanks!! :)

  20. anonymous
    • 5 years ago
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    Glad to help :)

  21. anonymous
    • 5 years ago
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    okay last one please?

  22. anonymous
    • 5 years ago
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    New thread.

  23. anonymous
    • 5 years ago
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    \[Let f(x)=5^1/3+x^2.For what values of x does the instantaneous rate of chnage equal when the rate of change is 3.119?\]

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