Answer
$\frac{\Delta y}{\Delta t}=0$
Work Step by Step
*Average rates of change:
The average rate of change of $y=f(x)$ with respect to $x$ over the interval $[x_1,x_2]$ is:
$$\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2-x_1}$$
$$P(\theta)=\theta^3-4\theta^2+5\theta\hspace{1cm}[1,2]$$
The average rate of change of $y=P(\theta)$: $$\frac{\Delta y}{\Delta\theta}=\frac{(2^3-4\times2^2+5\times2)-(1^3-4\times1^2+5\times1)}{2-1}$$
$$\frac{\Delta y}{\Delta t}=\frac{(8-16+10)-(1-4+5)}{1}=2-2=0$$
