Questions: Consider the function: (g(x)=4 x^2-2 x+1) Find the average rate of change of (g(x)) between the points (x=-1) and (x=2) . Give your answer as an integer or reduced fraction.

$Consider the function: (g(x)=4 x^2-2 x+1) Find the average rate of change of (g(x)) between the points (x=-1) and (x=2) . Give your answer as an integer or reduced fraction.$

Transcript text: Consider the function: $g(x)=4 x^{2}-2 x+1$ Find the average rate of change of $g(x)$ between the points $x=-1$ and $x=2$ . Give your answer as an integer or reduced fraction. $\square$ Submit Question

Solution

Solution Steps

Step 1: Calculate $ g(-1) $

To find the average rate of change, we first need to evaluate the function $ g(x) $ at $ x = -1 $: \[ g(-1) = 4(-1)^2 - 2(-1) + 1 = 4(1) + 2 + 1 = 4 + 2 + 1 = 7. \]

Step 2: Calculate $ g(2) $

Next, evaluate the function $ g(x) $ at $ x = 2 $: \[ g(2) = 4(2)^2 - 2(2) + 1 = 4(4) - 4 + 1 = 16 - 4 + 1 = 13. \]

Step 3: Compute the average rate of change

The average rate of change of $ g(x) $ between $ x = -1 $ and $ x = 2 $ is given by: \[ \text{Average rate of change} = \frac{g(2) - g(-1)}{2 - (-1)} = \frac{13 - 7}{2 + 1} = \frac{6}{3} = 2. \]