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Chapter 2: Q5 (page 197)

Why does it make graphical sense that the derivative of a constant is zero? That the derivative of the identity function is constantly equal to 1? That the derivative of a linear function f (x) = mx + b is equal to m ?

Short Answer

Expert verified

The graph of derivative of constant function is a horizontal line that is y axis .

Derivative of identity function is 1. The rate of change of y with respect to x is 1.

Derivative of linear function is 'm'. The rate of change of y with respect to x is 'm'

Step by step solution

01

Given Information 

the derivative of a constant is zero

the derivative of the identity function is constantly equal to 1

the derivative of a linear function f (x) = mx + b is equal to m

02

Constant function 

Consider a function f(x) = k

Derivative of a constant function is always 0

f'(x)=0

y=0

The graph of y=0 is a horizontal line that is y axis .

03

Identity function 

Lets consider and identity function

f(x)=x

Derivative of f(x)=x is 1

Derivative of x is 1.

Derivative of identity function is 1. The rate of change of y with respect to x is 1.

04

Linear function 

consider a linear function f(x)=mx+b

When we differentiate with respect to x

f'(x)=m

Derivative of linear function is 'm'. The rate of change of y with respect to x is 'm'

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