Question

how do you compute delta y / delta x for the interval [2,5] where y = 4x-9? what is the instantaneous rate of change of y with respect to x at x=2?

Answer 1

\(\dfrac{\Delta y}{\Delta x}\) is the average rate of change of a function over an interval \([a,b]\), where \(\Delta x=b-a\) and \(\Delta y=y(b)-y(a)\).

In this case,
\[\dfrac{\Delta y}{\Delta x}=\frac{(4(5)-9)-(4(2)-9)}{5-2}\]