1. concavity

Without using a calculator, find the values of x for which the graph of y=x^3 - 6x^2 is concave downward.

Thanks

2. Hello, DINOCALC09!

It's pretty straight-foward.

Find the values of x for which the graph of $y\:=\:x^3 - 6x^2$ is concave downward.

First derivative: . $y' \:=\:3x^2 - 6x$

Second Derivative: . $y'' \:=\:6x-6$

The graph is concave down when the second derivative is negative.

So we have: . $6x-6 \:< \:0\quad\Rightarrow\quad x \:< \:1$

The graph is concave down for $x \in (-\infty,\,1)$

3. i believe that you messed up on the first derivative and hence the concave down part is x< 2

am i right?

4. Originally Posted by DINOCALC09
i believe that you messed up on the first derivative and hence the concave down part is x< 2

am i right?
yes you are..