Remember when determining concavity, you use the same method as finding maximum and minimum using the first derivative test, except now you used the second derivative.

For example, suppose the function if f(x) = x^3 + 2x^2 - 5x

f'(x) = 3x^2 +4x - 5

f''(x) = 6x + 4

6x + 4 = 0

6x = -4

x = -2/3

Now test a point on both sides of -2/3, we'll use -1 and 0

f''(-2) = 6(-2) + 4 = -8

f''(0) = 6(0) + 4 = 4

that means we have concave down from (-infinity, -2/3) and concave up from (-2/3, infinity)

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