Calculus Examples

$f (X) = x^{2} + \frac{360}{x}$

Step 1

Find the first derivative of the function.

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Step 1.1

By the Sum Rule, the derivative of $x^{2} + \frac{360}{x}$ with respect to $X$ is $\frac{d}{d X} [x^{2}] + \frac{d}{d X} [\frac{360}{x}]$ .

$\frac{d}{d X} [x^{2}] + \frac{d}{d X} [\frac{360}{x}]$

Step 1.2

Since $x^{2}$ is constant with respect to $X$ , the derivative of $x^{2}$ with respect to $X$ is $0$ .

$0 + \frac{d}{d X} [\frac{360}{x}]$

Step 1.3

Since $\frac{360}{x}$ is constant with respect to $X$ , the derivative of $\frac{360}{x}$ with respect to $X$ is $0$ .

$0 + 0$

Step 1.4

Add $0$ and $0$ .

$0$

Step 2

Since $0$ is constant with respect to $X$ , the derivative of $0$ with respect to $X$ is $0$ .

$f'' (X) = 0$

Step 3

To find the local maximum and minimum values of the function, set the derivative equal to $0$ and solve.

$0 = 0$

Step 4

Since there is no value of $x$ that makes the first derivative equal to $0$ , there are no local extrema.

No Local Extrema

Step 5

No Local Extrema