Questions: Find the average rate of change of the given function on the interval [1,6]. g(x)=2 x^2-x Select the correct answer below: 15 16 13 11 12

Solution Steps

To find the average rate of change of the function \( g(x) = 2x^2 - x \) on the interval \([1, 6]\), we need to calculate the difference in the function values at the endpoints of the interval and divide by the length of the interval. Specifically, we will compute \(\frac{g(6) - g(1)}{6 - 1}\).

We need to evaluate the function \( g(x) = 2x^2 - x \) at the endpoints of the interval \([1, 6]\).

Calculating \( g(1) \): \[ g(1) = 2(1)^2 - 1 = 2 - 1 = 1 \]

Calculating \( g(6) \): \[ g(6) = 2(6)^2 - 6 = 2(36) - 6 = 72 - 6 = 66 \]

The average rate of change of the function on the interval \([1, 6]\) is given by the formula: \[ \text{Average Rate of Change} = \frac{g(6) - g(1)}{6 - 1} \]

Substituting the values we found: \[ \text{Average Rate of Change} = \frac{66 - 1}{6 - 1} = \frac{65}{5} = 13 \]

Final Answer