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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 4, Problem 6RCC

**(a)**

To determine

**To state:** The First derivative test.

Expert Solution

**The first derivative test:**

“Suppose that *c* is a critical number of a continuous function *f* :

(a) If
*c*, then *f* has a local maximum at *c.*

(b) If
*c*, then *f* has a local minimum at *c.*

(c) If
*c*, or negative to the left and right of *c*, then *f* has no local maximum or minimum at *c”.*

**(b)**

To determine

**To state:** The second derivative test.

Expert Solution

**The second derivative test:**

“Suppose.
*c.*

(a) If
*f* has a local minimum at *c.*

(b) If
*f* has a local maximum at *c”.*

**(c)**

To determine

**To explain:** The relative advantages and disadvantages of first and second derivative tests.

Expert Solution

First derivative test guarantees the local maxima or minima of a function at a point. But if the second derivative of a function is zero then this test fails to conclude about local maxima or minima.

First derivative test is time consuming and its process is lengthy. Also it is necessary to check the behavior of a function over the intervals. Whereas the second derivative test is less time consuming than the first derivative test.