CPM Homework Help : CALC Problem 3-183

Determine algebraically whether $y = 2x^3-5x^2 + 1$ is concave up or concave down at $x = 0$ and at $x = 2$ . Then, verify your solution with a graph of $y ^ { \prime \prime }$ .

Hint 1:

A function is concave up when its $2$ nd-derivative is positive and concave down when its $2$ nd-derivative is negative.

Hint 2:

$y = 2x^³-5x^² + 1$
$y^\prime = 6x^²-10x$
$y^{\prime\prime} = 12x-10$