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Chapter 12: Q. 8 (page 988)

Fill in the blanks to complete each of the following theorem statements:

If f(x,y)has a local extremum at x0,y0, then x0,y0is a _____ of f.

Short Answer

Expert verified

If f(x,y)has a local extremum at x0,y0, then x0,y0is a critical pointof f.

Step by step solution

01

Step 1. Given information

If f(x,y)has a local extremum at x0,y0, then x0,y0is a _____ of f.

02

Step 2. Filling in the blanks

If f(x,y)has a local extremum at x0,y0, then x0,y0 is a critical point of f.

This is because a local extremum can occur only at a critical point. A point x0,y0in the domain of a function f(x,y)is called a critical point of fif x0,y0is a stationary point of for if fis not differentiable at x0,y0.

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