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Graphing y = 0,80*x+0,48*x+0,02

Function f()

The graph:

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Intersection points:

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The solution

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       4*x   12*x   1 
f(x) = --- + ---- + --
        5     25    50
$$f{\left(x \right)} = \left(\frac{12 x}{25} + \frac{4 x}{5}\right) + \frac{1}{50}$$
f = 12*x/25 + 4*x/5 + 1/50
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:
$$\left(\frac{12 x}{25} + \frac{4 x}{5}\right) + \frac{1}{50} = 0$$
Solve this equation
The points of intersection with the axis X:

Analytical solution
$$x_{1} = - \frac{1}{64}$$
Numerical solution
$$x_{1} = -0.015625$$
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to 4*x/5 + 12*x/25 + 1/50.
$$\left(\frac{0 \cdot 4}{5} + \frac{0 \cdot 12}{25}\right) + \frac{1}{50}$$
The result:
$$f{\left(0 \right)} = \frac{1}{50}$$
The point:
(0, 1/50)
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
$$\frac{32}{25} = 0$$
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
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty}\left(\left(\frac{12 x}{25} + \frac{4 x}{5}\right) + \frac{1}{50}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\left(\frac{12 x}{25} + \frac{4 x}{5}\right) + \frac{1}{50}\right) = \infty$$
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 4*x/5 + 12*x/25 + 1/50, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\left(\frac{12 x}{25} + \frac{4 x}{5}\right) + \frac{1}{50}}{x}\right) = \frac{32}{25}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = \frac{32 x}{25}$$
$$\lim_{x \to \infty}\left(\frac{\left(\frac{12 x}{25} + \frac{4 x}{5}\right) + \frac{1}{50}}{x}\right) = \frac{32}{25}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = \frac{32 x}{25}$$
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:
$$\left(\frac{12 x}{25} + \frac{4 x}{5}\right) + \frac{1}{50} = \frac{1}{50} - \frac{32 x}{25}$$
- No
$$\left(\frac{12 x}{25} + \frac{4 x}{5}\right) + \frac{1}{50} = \frac{32 x}{25} - \frac{1}{50}$$
- No
so, the function
not is
neither even, nor odd
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