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5*x f(x) = - --- + 11 12

$$f{\left(x \right)} = 11 - \frac{5 x}{12}$$

f = 11 - 5*x/12

The graph of the function

The points of intersection with the X-axis coordinate

Graph of the function intersects the axis X at f = 0

so we need to solve the equation:

$$11 - \frac{5 x}{12} = 0$$

Solve this equation

The points of intersection with the axis X:

**Analytical solution**

$$x_{1} = \frac{132}{5}$$

**Numerical solution**

$$x_{1} = 26.4$$

so we need to solve the equation:

$$11 - \frac{5 x}{12} = 0$$

Solve this equation

The points of intersection with the axis X:

$$x_{1} = \frac{132}{5}$$

$$x_{1} = 26.4$$

Extrema of the function

In order to find the extrema, we need to solve the equation

$$\frac{d}{d x} f{\left(x \right)} = 0$$

(the derivative equals zero),

and the roots of this equation are the extrema of this function:

$$\frac{d}{d x} f{\left(x \right)} = $$

the first derivative

$$- \frac{5}{12} = 0$$

Solve this equation

Solutions are not found,

function may have no extrema

$$\frac{d}{d x} f{\left(x \right)} = 0$$

(the derivative equals zero),

and the roots of this equation are the extrema of this function:

$$\frac{d}{d x} f{\left(x \right)} = $$

the first derivative

$$- \frac{5}{12} = 0$$

Solve this equation

Solutions are not found,

function may have no extrema

Inflection points

Let's find the inflection points, we'll need to solve the equation for this

$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$

(the second derivative equals zero),

the roots of this equation will be the inflection points for the specified function graph:

$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$

the second derivative

$$0 = 0$$

Solve this equation

Solutions are not found,

maybe, the function has no inflections

$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$

(the second derivative equals zero),

the roots of this equation will be the inflection points for the specified function graph:

$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$

the second derivative

$$0 = 0$$

Solve this equation

Solutions are not found,

maybe, the function has no inflections

Horizontal asymptotes

Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo

$$\lim_{x \to -\infty}\left(11 - \frac{5 x}{12}\right) = \infty$$

Let's take the limit

so,

horizontal asymptote on the left doesn’t exist

$$\lim_{x \to \infty}\left(11 - \frac{5 x}{12}\right) = -\infty$$

Let's take the limit

so,

horizontal asymptote on the right doesn’t exist

$$\lim_{x \to -\infty}\left(11 - \frac{5 x}{12}\right) = \infty$$

Let's take the limit

so,

horizontal asymptote on the left doesn’t exist

$$\lim_{x \to \infty}\left(11 - \frac{5 x}{12}\right) = -\infty$$

Let's take the limit

so,

horizontal asymptote on the right doesn’t exist

Inclined asymptotes

Inclined asymptote can be found by calculating the limit of -5*x/12 + 11, divided by x at x->+oo and x ->-oo

$$\lim_{x \to -\infty}\left(\frac{11 - \frac{5 x}{12}}{x}\right) = - \frac{5}{12}$$

Let's take the limit

so,

inclined asymptote equation on the left:

$$y = - \frac{5 x}{12}$$

$$\lim_{x \to \infty}\left(\frac{11 - \frac{5 x}{12}}{x}\right) = - \frac{5}{12}$$

Let's take the limit

so,

inclined asymptote equation on the right:

$$y = - \frac{5 x}{12}$$

$$\lim_{x \to -\infty}\left(\frac{11 - \frac{5 x}{12}}{x}\right) = - \frac{5}{12}$$

Let's take the limit

so,

inclined asymptote equation on the left:

$$y = - \frac{5 x}{12}$$

$$\lim_{x \to \infty}\left(\frac{11 - \frac{5 x}{12}}{x}\right) = - \frac{5}{12}$$

Let's take the limit

so,

inclined asymptote equation on the right:

$$y = - \frac{5 x}{12}$$

Even and odd functions

Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).

So, check:

$$11 - \frac{5 x}{12} = \frac{5 x}{12} + 11$$

- No

$$11 - \frac{5 x}{12} = - \frac{5 x}{12} - 11$$

- No

so, the function

not is

neither even, nor odd

So, check:

$$11 - \frac{5 x}{12} = \frac{5 x}{12} + 11$$

- No

$$11 - \frac{5 x}{12} = - \frac{5 x}{12} - 11$$

- No

so, the function

not is

neither even, nor odd