Find the Average Rate of Change f(x)=x^2-x , x=1 , x=5

$f (x) = x^{2} - x$ , $x = 1$ , $x = 5$

Step 1

Substitute using the average rate of change formula.

The average rate of change of a function can be found by calculating the change in $y$ values of the two points divided by the change in $x$ values of the two points.

$\frac{f (5) - f (1)}{(5) - (1)}$

Substitute the equation $y = x^{2} - x$ for $f (5)$ and $f (1)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{({(5)}^{2} - (5)) - ({(1)}^{2} - (1))}{(5) - (1)}$

Step 2

Simplify the expression.

Simplify the numerator.

Raise $5$ to the power of $2$ .

$\frac{25 - (5) - (1^{2} - (1))}{5 - (1)}$

Multiply $- 1$ by $5$ .

$\frac{25 - 5 - (1^{2} - (1))}{5 - (1)}$

Simplify each term.

One to any power is one.

$\frac{25 - 5 - (1 - (1))}{5 - (1)}$

Multiply $- 1$ by $1$ .

$\frac{25 - 5 - (1 - 1)}{5 - (1)}$

Subtract $1$ from $1$ .

$\frac{25 - 5 - 0}{5 - (1)}$

Multiply $- 1$ by $0$ .

$\frac{25 - 5 + 0}{5 - (1)}$

Add $25 - 5$ and $0$ .

$\frac{25 - 5}{5 - (1)}$

Subtract $5$ from $25$ .

$\frac{20}{5 - (1)}$

Simplify the denominator.

Multiply $- 1$ by $1$ .

$\frac{20}{5 - 1}$

Subtract $1$ from $5$ .

$\frac{20}{4}$

Divide $20$ by $4$ .

$5$

Find the Average Rate of Change f(x)=x^2-x , x=1 , x=5

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