anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
What is f'(x)?
anonymous
  • anonymous
\[f(x)=x^3+Ax^2+Bx-15\]
anonymous
  • anonymous
sorry i miss read that.

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anonymous
  • anonymous
Now find f'(x).
anonymous
  • anonymous
f'(x)=\[3x^2+2Ax+B\]
anonymous
  • anonymous
and then f''(x)
anonymous
  • anonymous
\[f"(x)=6x+2A\]
anonymous
  • anonymous
OKay so how do we find the maxima of a polynomial?
anonymous
  • anonymous
Am I suppose to plug something in?
anonymous
  • anonymous
yes that's right :)
anonymous
  • anonymous
So I plug the two into the original function right? Then plug the 3 into the second derivative?
anonymous
  • anonymous
Do you know what is inflection point and critical points?
anonymous
  • anonymous
Critical values are the zeros of the 1st dervivative and inflection points are the zeros of the 2nd derivative?
anonymous
  • anonymous
Yes for the first but for the second that is only necessary condition but not sufficient condition.
anonymous
  • anonymous
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.
anonymous
  • anonymous
So what do I need to do? I'm confused now
anonymous
  • anonymous
If I haven't made any error then \( A=-9 \) and you can find B accordingly :)
anonymous
  • anonymous
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
anonymous
  • anonymous
aha! I understand thanks!! :)
anonymous
  • anonymous
Glad to help :)
anonymous
  • anonymous
okay last one please?
anonymous
  • anonymous
New thread.
anonymous
  • anonymous
\[Let f(x)=5^1/3+x^2.For what values of x does the instantaneous rate of chnage equal when the rate of change is 3.119?\]

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