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

3-183.

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

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

*y* = 2*x*³ − 5*x*² + 1 *y* ' = 6*x*² - 10*x* *y* '' = 12*x* - 10