Questions: Find the average rate of change of g(x)=2x^2+10 from x=3 to x=7. Simplify your answer as much as possible.

Transcript text: Find the average rate of change of $g(x)=2 x^{2}+10$ from $x=3$ to $x=7$. Simplify your answer as much as possible.

Solution

Solution Steps

Step 1: Define the function and the interval

The function given is $f(x)$, and we are interested in the interval from $x=3$ to $x=7$.

Step 2: Apply the formula for the average rate of change

The average rate of change of a function $f(x)$ from $x=a$ to $x=b$ is given by the formula: $$ \text{Average rate of change} = \frac{f(b) - f(a)}{b - a} $$ Substituting the given values, we get: $$ \text{Average rate of change} = \frac{f({b}) - f({a})}{{{b} - {a}}} = \frac{{{f_b} - {f_a}}}{{{b} - {a}}} $$

Step 3: Calculate the average rate of change

After performing the calculation, the average rate of change is approximately 20.