Question

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

Answer 1

You're still not saying what actual difficulties you're having.

Do you know how to find inflection points?

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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