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

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- Apr 19th 2009, 04:28 PMvenikUSAwhen the f(x) positive, negative, or zero
How to determine, when the first and second derivatives of f(x) is positive, negative, or zero.

- Apr 19th 2009, 04:34 PMmollymcf2009

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.