Thread: when the f(x) positive, negative, or zero

How to determine, when the first and second derivatives of f(x) is positive, negative, or zero.

Originally Posted by venikUSA

How to determine, when the first and second derivatives of f(x) is positive, negative, or zero.

When f(x) is increasing, f ' (x) will be positive

When f(x) is decreasing, f ' (x) will be negative

When f(x) is concave down, f '' (x) will be negative

When f(x) is concave up, f '' (x) will be positive

When f(x) changed from increasing to decreasing (or vice versa) f ' (x) = 0

When f(x) changes in concavity, f '' (x)= 0

If it helps you, graph all three on the same graph and look at what changes.