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)
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You're still not saying what actual difficulties you're having.
Do you know how to find inflection points?
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.
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.