Question

What is the average rate of change for f(z)=2z^2+4z-3 over the interval [-1, 4]

Answer 1

Given:

Function  $f(z)=2z^{2} +4z-3$ defined in the interval $[-1,4]$

To Find:

We have to find the average rate of change of function.

Solution:

We know that instantaneous rate of change is given by $\frac{dy}{dx}$ at any given point.

Let $f(z)=y$

So, Rate of change at any point is obtained by differentiating the equation with respect to z. Let that equation be $g(z)= 4z+4$

The average value is given by $\frac{delta. y}{delta. x}$

Therefore, we need to find average value of $g(z)$ over $[-1,4]$

Hence, our answer is, $\frac{g(4)-g(-1)}{4-(-1)}$

$= \frac{{4(4)+4}-{4(-1)+4}}{5} \\=\frac{16+4+4-4}{5} \\=\frac{20}{5} \\=4$

Hence, the average rate of change of function f over the interval $[-1,4]$ is 4.