# Math Help - equation of the line tangent to a curve at its inflection point

1. ## equation of the line tangent to a curve at its inflection point

An equation of the line tangent to the graph of y=a^3+ax^2+2 at its point of inflection is:?

i have no idea.
i know you do something with the second derivative and find where it goes from concave upward to concave downward.
but whats with the equation?
I am sure that you mean $a {\color{red}x^3} +ax^2 +2$
Slope: $m=3ax^2+2ax$.
Second derivative: $6ax+2a$
Then inflection point: $6x + 2a = 0\; \Rightarrow \;x = \frac{{ - 1}}{3}$.
The point is $\left( {\frac{{ - 1}}{3},\frac{{2a}}{{27}} + 2} \right)$ and slope is $m=\frac{-a}{3}$