anonymous
  • anonymous
for what value(s) of k will f(x)=x^3-kx^2+kx+k have an inflection point at x=5?
MIT 18.01 Single Variable Calculus (OCW)
katieb
  • katieb
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anonymous
  • anonymous
You're still not saying what actual difficulties you're having. Do you know how to find inflection points?
anonymous
  • anonymous
If you wish to find inflection points, just take the structural form of the derivative (its formula) and find the places where it equals zero. An inflection point will be a point with zero derivative and with derivatives of different signs before and after it.
anonymous
  • anonymous
No, JulioMarco, those aren't inflection points. Those are maxima and minima you're describing. At an inflection point, it's the second derivative that's zero, since a function's inflection points are at maxima and minima of its first derivative. An inflection point of f(x) at x will be a maximum or minimum of f'(x) at x, and so f''(x)=0 at x.

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anonymous
  • anonymous
SomeBloke is right, its when d^2(f(x))/d(x^2)=0, inflections points are found by taking the 2nd derivative and setting them to 0.
anonymous
  • anonymous
SomeBloke and Asimo, you are completely right... I wrote it in the wrong way, thank you! :)

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