Questions: 3. Find the AROC on the interval [h, h + 2] for g(x) = 5 π

Transcript text: 3. Find the AROC on the interval [h, h + 2] for g(x) = 5 π

Solution

Solution Steps

To find the Average Rate of Change (AROC) of a constant function \( g(x) = 5\pi \) over an interval \([h, h+2]\), we use the formula for AROC: \(\frac{g(h+2) - g(h)}{(h+2) - h}\). Since \( g(x) \) is constant, \( g(h+2) = g(h) = 5\pi \), so the AROC will be zero.

Step 1: Define the Function

The function given is \( g(x) = 5\pi \), which is a constant function. This means that for any value of \( x \), the output will always be \( 5\pi \).

Step 2: Calculate \( g(h) \) and \( g(h+2) \)

For the interval \([h, h+2]\):

\( g(h) = 5\pi \)
\( g(h+2) = 5\pi \)

Step 3: Apply the AROC Formula

The Average Rate of Change (AROC) is calculated using the formula: \[ \text{AROC} = \frac{g(h+2) - g(h)}{(h+2) - h} \] Substituting the values we found: \[ \text{AROC} = \frac{5\pi - 5\pi}{(h+2) - h} = \frac{0}{2} = 0 \]