   Chapter 14, Problem 9RCC

Chapter
Section
Textbook Problem

(a) What does it mean to say that f is differentiable at (a, b)?(b) How do you usually verify that f is differentiable?

(a)

To determine

To Describe: The meaning of f is differentiable at (a,b).

Explanation

Consider the function, z=f(x,y).

Let (a,b) arbitrary point. If the function z=f(x,y) satisfies the below three conditions then the function z=f(x,y) is differentiable at (a,b).

Condition 1:

The partial differentiable of fx(x,y)andfy(x,y) exist at (a,b).

Condition 2:

The value of ΔxandΔy exist

(b)

To determine

To verify:f is differentiable.

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