CPM Homework Help : APCALC Problem 3-183

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

Hint:

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

Hint:

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