Mister Exam

Other calculators

  • How to use it?

  • Graphing y =:
  • x^2-5x-3
  • x^2-3x+3
  • -x^2-3
  • -x²+2x+3

  • Identical expressions

  • two *x^ two /x^ three
  • 2 multiply by x squared divide by x cubed
  • two multiply by x to the power of two divide by x to the power of three
  • 2*x2/x3
  • 2*x²/x³
  • 2*x to the power of 2/x to the power of 3
  • 2x^2/x^3
  • 2x2/x3
  • 2*x^2 divide by x^3
Plotting a function graph/ 2*x^2/x^3

Graphing y = 2*x^2/x^3

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
          2
       2*x 
f(x) = ----
         3 
        x
f(x)=2x2x3f{\left(x \right)} = \frac{2 x^{2}}{x^{3}} 
f = (2*x^2)/x^3
The graph of the function
0-50-40-30-20-105010203040-500500
The domain of the function
The points at which the function is not precisely defined:
x1=0x_{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:
2x2x3=0\frac{2 x^{2}}{x^{3}} = 0
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (2*x^2)/x^3.
2⋅0203\frac{2 \cdot 0^{2}}{0^{3}}
The result:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- the solutions of the equation d'not exist
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\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:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
−6x2+4xx3=0- \frac{6}{x^{2}} + \frac{4 x}{x^{3}} = 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
d2dx2f(x)=0\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:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
4x3=0\frac{4}{x^{3}} = 0
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
x1=0x_{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→−∞(2x2x3)=0\lim_{x \to -\infty}\left(\frac{2 x^{2}}{x^{3}}\right) = 0
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=0y = 0
lim⁡x→∞(2x2x3)=0\lim_{x \to \infty}\left(\frac{2 x^{2}}{x^{3}}\right) = 0
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=0y = 0
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of (2*x^2)/x^3, divided by x at x->+oo and x ->-oo
lim⁡x→−∞(2xx3)=0\lim_{x \to -\infty}\left(\frac{2 x}{x^{3}}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(2xx3)=0\lim_{x \to \infty}\left(\frac{2 x}{x^{3}}\right) = 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:
2x2x3=−2x\frac{2 x^{2}}{x^{3}} = - \frac{2}{x}
- No
2x2x3=2x\frac{2 x^{2}}{x^{3}} = \frac{2}{x}
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator