   Chapter 14, Problem 15RCC

Chapter
Section
Textbook Problem

What do the following statements mean?(a) f has a local maximum at (a, b).(b) f has an absolute maximum at (a, b).(c) f has a local minimum at (a, b).(d) f has an absolute minimum at (a, b).(e) f has a saddle point at (a, b).

(a)

To determine

To describe: The meaning of, “f has a local maximum at (a,b) ”.

Explanation

Let the function be f(x,y) .

The function f(x,y) has local maximum at (a,b) if the functional value of f(x,y) is less than or equal to the the functional value of f(a,b)

(b)

To determine

To describe: The meaning of, “f has an absolute maximum at (a,b) ”.

(c)

To determine

To describe: The meaning of, “f has a local minimum at (a,b) ”.

(d)

To determine

To describe: The meaning of, “f has an absolute minimum at (a,b) ”.

(e)

To determine

To describe: The meaning of,“f has a saddle point at (a,b) ”.

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