Question

Find the average rate of change of the function from alt="x_{1}" align="absmiddle" class="latex-formula">= 1 to $x_{2}$ = 5.​
Function = $x^{2}$ - 4x + 10

Answer 1

Hi there!

$\large\boxed{\text{Average rate} = 2}$

Use the following equation to solve:

$\text{Average rate} = \frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}$

Solve for the y-values of the equation at the given x values:

f(1) = 1² - 4(1) + 10 = 7

f(5) = 5² - 4(5) + 10 = 15

Plug  the solved values into the equation:

$\text{Average rate} = \frac{15 - 7}{5-1}$

Simplify:

$\text{Average rate} = \frac{8}{4} = 2$