Calculus Course/Change in Variable

A Change in variable is a term used to express the difference between 2 variables . Let ${\displaystyle \Delta }$ represents Change in 2 variables ${\displaystyle x_{0}}$ and ${\displaystyle x}$ then

${\displaystyle \Delta x=x-x_{0}}$

${\displaystyle x=x_{0}+\Delta x}$

If there is a function ${\displaystyle f(x)}$ such that when ${\displaystyle x}$ change by an amount ${\displaystyle \Delta x}$ the change in function will be

${\displaystyle \Delta f(x)=f(x)-f(x_{0})}$

${\displaystyle f(x)=f(x_{0})+\Delta f(x)}$

There are 2 points (1,3) (5,7) then

${\displaystyle \Delta x=x-x_{0}=5-1=4}$

${\displaystyle \Delta f(x)=7-3=4}$