Mister Exam
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-
How to use it?
- Graphing y =:
- x/(4-x^2)
- -x^4+x^2+5
- |x|+4
- x^4-5x^2+6
- Derivative of:
-
-x/5
- Limit of the function:
-
-x/5
-
Identical expressions
- -x/ five
- minus x divide by 5
- minus x divide by five
- -x divide by 5
-
Similar expressions
- (4*(x-600)^3+3*1200^(3/2)+12*x/5)/(3*1200^(3/2)-4*(x-600)^3+12*(1200-x)/5)
- (5-x)/(5+x)
- sqrt(x^2+81)/4+(15-x)/5
- 134.148/((3000-x)/537+537/(3000-x))
- x/5
Graphing y = -x/5
The solution
You have entered
[src]
-x
f(x) = ---
5
$$f{\left(x \right)} = \frac{\left(-1\right) x}{5}$$
f = (-x)/5
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:
$$\frac{\left(-1\right) x}{5} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 0$$
Numerical solution
$$x_{1} = 0$$
so we need to solve the equation:
$$\frac{\left(-1\right) x}{5} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 0$$
Numerical solution
$$x_{1} = 0$$
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
$$- \frac{1}{5} = 0$$
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
$$- \frac{1}{5} = 0$$
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
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) x}{5}\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{5}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) x}{5}\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{5}\right) = -\infty$$
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 (-x)/5, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty} - \frac{1}{5} = - \frac{1}{5}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - \frac{x}{5}$$
$$\lim_{x \to \infty} - \frac{1}{5} = - \frac{1}{5}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = - \frac{x}{5}$$
$$\lim_{x \to -\infty} - \frac{1}{5} = - \frac{1}{5}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - \frac{x}{5}$$
$$\lim_{x \to \infty} - \frac{1}{5} = - \frac{1}{5}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = - \frac{x}{5}$$
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:
$$\frac{\left(-1\right) x}{5} = \frac{x}{5}$$
- No
$$\frac{\left(-1\right) x}{5} = - \frac{x}{5}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\frac{\left(-1\right) x}{5} = \frac{x}{5}$$
- No
$$\frac{\left(-1\right) x}{5} = - \frac{x}{5}$$
- No
so, the function
not is
neither even, nor odd