Without using a calculator, find the values of x for which the graph of y=x^3 - 6x^2 is concave downward.
Thanks
Hello, DINOCALC09!
It's pretty straight-foward.
Exactly where is your difficulty?
Find the values of x for which the graph of $\displaystyle y\:=\:x^3 - 6x^2$ is concave downward.
First derivative: .$\displaystyle y' \:=\:3x^2 - 6x$
Second Derivative: .$\displaystyle y'' \:=\:6x-6$
The graph is concave down when the second derivative is negative.
So we have: .$\displaystyle 6x-6 \:< \:0\quad\Rightarrow\quad x \:< \:1$
The graph is concave down for $\displaystyle x \in (-\infty,\,1)$