Question

Find the average rate of change from 0 to pi/2.

Answer 1

Main Answer:

The average rate of change of a function from
`\(x=a\) to \(x=b\)` is given by the formula:

`\[ \text{Average Rate of Change} = (f(b) - f(a))/(b - a) \]`

To find the average rate of change from 0 to
`\((\pi)/(2)\)` for a given function, we substitute
`\(a=0\) and \(b=(\pi)/(2)\)` into the formula and compute the result.

Step-by-step explanation:

Let's consider a function
`\(f(x)\)` for which we want to find the average rate of change from 0 to
`\((\pi)/(2)\)`. The formula for average rate of change is:

`\[ \text{Average Rate of Change} = (f\left((\pi)/(2)\right) - f(0))/((\pi)/(2) - 0) \]`

If you have the specific function
`\(f(x)\)`, you would substitute
`\(x=(\pi)/(2)\) and \(x=0\)` into the function, subtract the results, and then divide by
`\((\pi)/(2)\)`.

The resulting value would be the average rate of change over the given interval.