What are the points of inflection, if any, of f(t) = 4t^3 + 3t^2 - 6t +1 ?

1 Answer
Feb 26, 2016

Inflection point is at $t = - \frac{1}{4}$

Explanation:

$f ' \left(t\right) = 12 {t}^{2} + 6 t - 6$

$f ' ' \left(t\right) = 24 t + 6$

A necessary condition for a point of inflection is that $f ' ' \left(t\right) = 0$.

Accordingly, there would be inflection point at 24t+6=0 , that is $t = - \frac{1}{4}$