How do you find the inflection points of the graph of the function: $f(x)=x^4-6x^3$ ?

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Answer 1 · 2015-08-11T09:03:22

$x = 0, f(0) = 0 " and " x = 3, f(3) = -81$

A point of inflection can be found when the second derivative of f(x) is equal to zero i.e. $(d^2f)/dx^2 = 0$ .

$f(x) = x^4-6x^3$
$(d^2f)/dx^2 = 12x(x-3) = 0$
$x = 0, f(0) = 0 " and " x = 3, f(3) = -81$

How do you find the inflection points of the graph of the function: f(x)=x^4-6x^3f(x)=x^4-6x^3?