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# (a) State the First Derivative Test.(b) State the Second Derivative Test. Under what circumstances is it inconclusive? What do you do if it fails?

## (a) If $f^{\prime}$ changes from positive to negative at $c,$ then $f$ has a local max at $c$ . If $f^{\prime}$ changes from negative to positive at $c,$ then $f$ has a local min at $c$ . If $f^{\prime}$ does not change sign at $c,$ then $f$ has no local max or min at $c$ .b) We used the concepts of first derivative and second derivative to solve this.Check inside for more details.

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Differentiation

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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Derivatives

Differentiation

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