Precalculus Examples

f (x) = 2 x^{2} - 4

$f (x) = 2 x^{2} - 4$ ,

[5, 6]

$[5, 6]$

Step 1

Write

f (x) = 2 x^{2} - 4

$f (x) = 2 x^{2} - 4$ as an equation.

y = 2 x^{2} - 4

$y = 2 x^{2} - 4$

Step 2

Substitute using the average rate of change formula.

Tap for more steps...

Step 2.1

The average rate of change of a function can be found by calculating the change in

y

$y$ values of the two points divided by the change in

x

$x$ values of the two points.

\frac{f (6) - f (5)}{(6) - (5)}

$\frac{f (6) - f (5)}{(6) - (5)}$

Step 2.2

Substitute the equation

y = 2 x^{2} - 4

$y = 2 x^{2} - 4$ for

f (6)

$f (6)$ and

f (5)

$f (5)$ , replacing

x

$x$ in the function with the corresponding

x

$x$ value.

\frac{(2 {(6)}^{2} - 4) - (2 {(5)}^{2} - 4)}{(6) - (5)}

$\frac{(2 {(6)}^{2} - 4) - (2 {(5)}^{2} - 4)}{(6) - (5)}$

\frac{(2 {(6)}^{2} - 4) - (2 {(5)}^{2} - 4)}{(6) - (5)}

$\frac{(2 {(6)}^{2} - 4) - (2 {(5)}^{2} - 4)}{(6) - (5)}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Raise

6

$6$ to the power of

2

$2$ .

\frac{2 \cdot 36 - 4 - (2 \cdot 5^{2} - 4)}{6 - (5)}

$\frac{2 \cdot 36 - 4 - (2 \cdot 5^{2} - 4)}{6 - (5)}$

Step 3.1.2

Multiply

2

$2$ by

36

$36$ .

\frac{72 - 4 - (2 \cdot 5^{2} - 4)}{6 - (5)}

$\frac{72 - 4 - (2 \cdot 5^{2} - 4)}{6 - (5)}$

Step 3.1.3

Simplify each term.

Tap for more steps...

Step 3.1.3.1

Raise

5

$5$ to the power of

2

$2$ .

\frac{72 - 4 - (2 \cdot 25 - 4)}{6 - (5)}

$\frac{72 - 4 - (2 \cdot 25 - 4)}{6 - (5)}$

Step 3.1.3.2

Multiply

2

$2$ by

25

$25$ .

\frac{72 - 4 - (50 - 4)}{6 - (5)}

$\frac{72 - 4 - (50 - 4)}{6 - (5)}$

\frac{72 - 4 - (50 - 4)}{6 - (5)}

$\frac{72 - 4 - (50 - 4)}{6 - (5)}$

Step 3.1.4

Subtract

4

$4$ from

50

$50$ .

\frac{72 - 4 - 1 \cdot 46}{6 - (5)}

$\frac{72 - 4 - 1 \cdot 46}{6 - (5)}$

Step 3.1.5

Multiply

- 1

$- 1$ by

46

$46$ .

\frac{72 - 4 - 46}{6 - (5)}

$\frac{72 - 4 - 46}{6 - (5)}$

Step 3.1.6

Subtract

4

$4$ from

72

$72$ .

\frac{68 - 46}{6 - (5)}

$\frac{68 - 46}{6 - (5)}$

Step 3.1.7

Subtract

46

$46$ from

68

$68$ .

\frac{22}{6 - (5)}

$\frac{22}{6 - (5)}$

\frac{22}{6 - (5)}

$\frac{22}{6 - (5)}$

Step 3.2

Simplify the denominator.

Tap for more steps...

Step 3.2.1

Multiply

- 1

$- 1$ by

5

$5$ .

\frac{22}{6 - 5}

$\frac{22}{6 - 5}$

Step 3.2.2

Subtract

5

$5$ from

6

$6$ .

\frac{22}{1}

$\frac{22}{1}$

\frac{22}{1}

$\frac{22}{1}$

Step 3.3

Divide

22

$22$ by

1

$1$ .

22

$22$

22

$22$

Enter YOUR Problem