Calculus Examples

$f (x) = \sqrt{3} x (2 x - \frac{2}{3})$ , $(- 4, 1)$

Step 1

Evaluate $f (x) = \sqrt{3} x (2 x - \frac{2}{3})$ at $x = - 4$ .

Tap for more steps...

Step 1.1

Replace the variable $x$ with $- 4$ in the expression.

$f (- 4) = \sqrt{3} (- 4) (2 (- 4) - \frac{2}{3})$

Step 1.2

Simplify the result.

Tap for more steps...

Step 1.2.1

Move $- 4$ to the left of $\sqrt{3}$ .

$f (- 4) = - 4 \cdot (\sqrt{3} (2 (- 4) - \frac{2}{3}))$

Step 1.2.2

Multiply $2$ by $- 4$ .

$f (- 4) = - 4 \sqrt{3} (- 8 - \frac{2}{3})$

Step 1.2.3

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$f (- 4) = - 4 \sqrt{3} (- 8 \cdot \frac{3}{3} - \frac{2}{3})$

Step 1.2.4

Combine $- 8$ and $\frac{3}{3}$ .

$f (- 4) = - 4 \sqrt{3} (\frac{- 8 \cdot 3}{3} - \frac{2}{3})$

Step 1.2.5

Combine the numerators over the common denominator.

$f (- 4) = - 4 \sqrt{3} \frac{- 8 \cdot 3 - 2}{3}$

Step 1.2.6

Simplify the numerator.

Tap for more steps...

Step 1.2.6.1

Multiply $- 8$ by $3$ .

$f (- 4) = - 4 \sqrt{3} \frac{- 24 - 2}{3}$

Step 1.2.6.2

Subtract $2$ from $- 24$ .

$f (- 4) = - 4 \sqrt{3} \frac{- 26}{3}$

Step 1.2.7

Move the negative in front of the fraction.

$f (- 4) = - 4 \sqrt{3} (- \frac{26}{3})$

Step 1.2.8

Multiply $- 4 \sqrt{3} (- \frac{26}{3})$ .

Tap for more steps...

Step 1.2.8.1

Multiply $- 1$ by $- 4$ .

$f (- 4) = 4 \sqrt{3} (\frac{26}{3})$

Step 1.2.8.2

Combine $\frac{26}{3}$ and $4$ .

$f (- 4) = \frac{26 \cdot 4}{3} \cdot \sqrt{3}$

Step 1.2.8.3

Multiply $26$ by $4$ .

$f (- 4) = \frac{104}{3} \cdot \sqrt{3}$

Step 1.2.8.4

Combine $\frac{104}{3}$ and $\sqrt{3}$ .

$f (- 4) = \frac{104 \sqrt{3}}{3}$

Step 1.2.9

The final answer is $\frac{104 \sqrt{3}}{3}$ .

$\frac{104 \sqrt{3}}{3}$

Step 2

Since $\frac{104 \sqrt{3}}{3}$ $\neq$ $1$ , the point is not on the graph.

The point is not on the graph

Step 3