Mister Exam
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-
How to use it?
- Graphing y =:
- -2x^2+4x+6
- y=-x^2+4-3
- y=|-2x|
- x/x
- Integral of d{x}:
-
x^(-3/4)
- Limit of the function:
-
x^(-3/4)
-
Identical expressions
- x^(- three / four)
- x to the power of ( minus 3 divide by 4)
- x to the power of ( minus three divide by four)
- x(-3/4)
- x-3/4
- x^-3/4
- x^(-3 divide by 4)
-
Similar expressions
- x^(3/4)
Graphing y = x^(-3/4)
The solution
You have entered
[src]
1
f(x) = ----
3/4
x
$$f{\left(x \right)} = \frac{1}{x^{\frac{3}{4}}}$$
f = x^(-3/4)
The graph of the function
The domain of the function
The points at which the function is not precisely defined:
$$x_{1} = 0$$
$$x_{1} = 0$$
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:
$$\frac{1}{x^{\frac{3}{4}}} = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
so we need to solve the equation:
$$\frac{1}{x^{\frac{3}{4}}} = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
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
$$- \frac{3}{4 x^{\frac{7}{4}}} = 0$$
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
$$- \frac{3}{4 x^{\frac{7}{4}}} = 0$$
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
$$\frac{21}{16 x^{\frac{11}{4}}} = 0$$
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
$$\frac{21}{16 x^{\frac{11}{4}}} = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
$$x_{1} = 0$$
$$x_{1} = 0$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty} \frac{1}{x^{\frac{3}{4}}} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{x \to \infty} \frac{1}{x^{\frac{3}{4}}} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = 0$$
$$\lim_{x \to -\infty} \frac{1}{x^{\frac{3}{4}}} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{x \to \infty} \frac{1}{x^{\frac{3}{4}}} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = 0$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of x^(-3/4), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty} \frac{1}{x^{\frac{7}{4}}} = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty} \frac{1}{x^{\frac{7}{4}}} = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{x \to -\infty} \frac{1}{x^{\frac{7}{4}}} = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty} \frac{1}{x^{\frac{7}{4}}} = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
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:
$$\frac{1}{x^{\frac{3}{4}}} = \frac{1}{\left(- x\right)^{\frac{3}{4}}}$$
- No
$$\frac{1}{x^{\frac{3}{4}}} = - \frac{1}{\left(- x\right)^{\frac{3}{4}}}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\frac{1}{x^{\frac{3}{4}}} = \frac{1}{\left(- x\right)^{\frac{3}{4}}}$$
- No
$$\frac{1}{x^{\frac{3}{4}}} = - \frac{1}{\left(- x\right)^{\frac{3}{4}}}$$
- No
so, the function
not is
neither even, nor odd