# What are the points of inflection, if any, of f(x)=14x^3+32x^2-15x+4 ?

Dec 4, 2017

Points of inflection involve the second derivative. This can be obtained by applying the power rule twice.

$f ' \left(x\right) = 42 {x}^{2} + 64 x - 15$

$f ' ' \left(x\right) = 84 x + 64$

When $f ' ' \left(x\right) = 0$, there will be points of inflection.

$0 = 84 x + 64$

$x = - \frac{16}{21}$

Hence, there will be a point of inflection when $x = - \frac{16}{21}$. Here is a graphical representation of the given function.

Hopefully this helps!