Fundamental Mathematics/Calculus/Rate of change

Rate of change

Rate of change

${\frac {\Delta f(x)}{\Delta x}}={\frac {f(x+\Delta x)-f(x)}{\Delta x}}=a$

From above,

$\Delta f(x)=a\Delta x$

$\Delta x={\frac {1}{a}}\Delta f(x)$

$f(x+\Delta x)=a\Delta x+f(x)$

Example

For any inclines linear motion, the slope of the line is

${\frac {\Delta v}{\Delta t}}={\frac {v-v_{o}}{t-t_{o}}}=a$

$\Delta v=a\Delta t$

$v-v_{o}=a(t-t_{o})$

$v=a(t-t_{o})+v_{o}$

Hence,

$v=at$ . ($t_{o}=0,v_{o}=0$)

$v=at+v_{o}$ . ($t_{o}=0$)

$v=v_{o}$ . ($a_{o}=0$)