### Home > CALC > Chapter 3 > Lesson 3.4.4 > Problem3-183

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 $y ^ { \prime \prime }$.

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

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