Ldaniel 2 years ago for what value(s) of k will f(x)=x^3-kx^2+kx+k have an inflection point at x=5?

1. SomeBloke

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

2. JulioMarco

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.

3. SomeBloke

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.

4. asimo3

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.

5. JulioMarco

SomeBloke and Asimo, you are completely right... I wrote it in the wrong way, thank you! :)