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Chapter 11: Q. 3 (page 871)

State what it means for a scalar function y=f(x) to be differentiable at a point c.

Short Answer

Expert verified

The limit obtained is called the derivate of f at c the process of finding the derivative of a function is a called differentiation

Step by step solution

01

Step 1. Given information

Given scalar functiony=f(x)

02

Step 2. The object is to define the differentiability of a scalar function y=f(x) at a point c.

Let x=cbe a point in the domain of the function f(x)

Iflimh鈫�0f(c+h)-f(c)h exists the we say thatf(x) is derivable at x=cand write

limh鈫�0f(c+h)-f(c)h=f'(c)or let x=cbe a point in the domain of the function f(x)

If limh鈫�0f(x)-f(a)x-aexists then we say that f(x)is derivate at x=cand limh鈫�0f(x)-f(c)x-c=f'(c)

The limit obtained is called the derivate of f at cthe process of finding the derivative of a function is a called differentiation

03

Step 3. Taking an example

Let f(x)=x2andC=2 in the domain off(x)

Consider limh鈫�0f(c+h)-f(c)h

=limh鈫�0f(2+h)-f(2)h=limh鈫�04h+h2h=limh鈫�04+h=4+0=4

exists

Thus the function is differentiable at 2

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Most popular questions from this chapter

Every description of the DNA molecule says that the strands of the helices run in opposite directions. This is meant as a statement about chemistry, not about the geometric shape of the double helix. Consider two helices

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