# How do you find the y coordinate of the inflection point of the function f(x)= 10(x-5)^3+2?

Apr 13, 2015

The inflection points of a function are the zeroes of the second derivative in which the sign of it change in sign.

So let's find the second derivative:

$y ' = 30 {\left(x - 5\right)}^{2}$

and

$y ' ' = 60 \left(x - 5\right)$.

Ther is only one zero: $x = 5$ and the second derivative change in sign in it, so $P \left(5 , 2\right)$ is the only inflection point, as you can see from the graph:

graph{10(x-5)^3 +2 [-10, 10, -5, 5]}