Calculus Examples

$f (\sqrt{3}) = 20 x^{4} - 120 x^{2}$

Step 1

Replace the variable $x$ with $\sqrt{3}$ in the expression.

$f (\sqrt{3}) = 20 {(\sqrt{3})}^{4} - 120 {(\sqrt{3})}^{2}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${\sqrt{3}}^{4}$ as $3^{2}$ .

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Step 2.1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$f (\sqrt{3}) = 20 {(3^{\frac{1}{2}})}^{4} - 120 {(\sqrt{3})}^{2}$

Step 2.1.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f (\sqrt{3}) = 20 \cdot 3^{\frac{1}{2} \cdot 4} - 120 {(\sqrt{3})}^{2}$

Step 2.1.1.3

Combine $\frac{1}{2}$ and $4$ .

$f (\sqrt{3}) = 20 \cdot 3^{\frac{4}{2}} - 120 {(\sqrt{3})}^{2}$

Step 2.1.1.4

Cancel the common factor of $4$ and $2$ .

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Step 2.1.1.4.1

Factor $2$ out of $4$ .

$f (\sqrt{3}) = 20 \cdot 3^{\frac{2 \cdot 2}{2}} - 120 {(\sqrt{3})}^{2}$

Step 2.1.1.4.2

Cancel the common factors.

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Step 2.1.1.4.2.1

Factor $2$ out of $2$ .

$f (\sqrt{3}) = 20 \cdot 3^{\frac{2 \cdot 2}{2 (1)}} - 120 {(\sqrt{3})}^{2}$

Step 2.1.1.4.2.2

Cancel the common factor.

$f (\sqrt{3}) = 20 \cdot 3^{\frac{2 \cdot 2}{2 \cdot 1}} - 120 {(\sqrt{3})}^{2}$

Step 2.1.1.4.2.3

Rewrite the expression.

$f (\sqrt{3}) = 20 \cdot 3^{\frac{2}{1}} - 120 {(\sqrt{3})}^{2}$

Step 2.1.1.4.2.4

Divide $2$ by $1$ .

$f (\sqrt{3}) = 20 \cdot 3^{2} - 120 {(\sqrt{3})}^{2}$

Step 2.1.2

Raise $3$ to the power of $2$ .

$f (\sqrt{3}) = 20 \cdot 9 - 120 {(\sqrt{3})}^{2}$

Step 2.1.3

Multiply $20$ by $9$ .

$f (\sqrt{3}) = 180 - 120 {(\sqrt{3})}^{2}$

Step 2.1.4

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 2.1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$f (\sqrt{3}) = 180 - 120 {(3^{\frac{1}{2}})}^{2}$

Step 2.1.4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f (\sqrt{3}) = 180 - 120 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 2.1.4.3

Combine $\frac{1}{2}$ and $2$ .

$f (\sqrt{3}) = 180 - 120 \cdot 3^{\frac{2}{2}}$

Step 2.1.4.4

Cancel the common factor of $2$ .

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Step 2.1.4.4.1

Cancel the common factor.

$f (\sqrt{3}) = 180 - 120 \cdot 3^{\frac{2}{2}}$

Step 2.1.4.4.2

Rewrite the expression.

$f (\sqrt{3}) = 180 - 120 \cdot 3$

Step 2.1.4.5

Evaluate the exponent.

$f (\sqrt{3}) = 180 - 120 \cdot 3$

Step 2.1.5

Multiply $- 120$ by $3$ .

$f (\sqrt{3}) = 180 - 360$

Step 2.2

Subtract $360$ from $180$ .

$f (\sqrt{3}) = - 180$

Step 2.3

The final answer is $- 180$ .

$- 180$

Step 3