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  • How to use it?

  • Graphing y =:
  • x^-6
  • x^3-x^2-x
  • x/(3+x^2)
  • (x+3)/(x+2)^2
  • Derivative of:
  • 2*sqrt(x^3) 2*sqrt(x^3)

  • Identical expressions

  • two *sqrt(x^ three)
  • 2 multiply by square root of (x cubed )
  • two multiply by square root of (x to the power of three)
  • 2*√(x^3)
  • 2*sqrt(x3)
  • 2*sqrtx3
  • 2*sqrt(x³)
  • 2*sqrt(x to the power of 3)
  • 2sqrt(x^3)
  • 2sqrt(x3)
  • 2sqrtx3
  • 2sqrtx^3
Plotting a function graph/ 2*sqrt(x^3)

Graphing y = 2*sqrt(x^3)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
            ____
           /  3 
f(x) = 2*\/  x
f(x)=2x3f{\left(x \right)} = 2 \sqrt{x^{3}} 
f = 2*sqrt(x^3)
The graph of the function
0.01.02.03.04.05.06.07.08.09.010.00100
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:
2x3=02 \sqrt{x^{3}} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
Numerical solution
x1=0x_{1} = 0
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to 2*sqrt(x^3).
2032 \sqrt{0^{3}}
The result:
f(0)=0f{\left(0 \right)} = 0
The point:
(0, 0)
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
3x3x=0\frac{3 \sqrt{x^{3}}}{x} = 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
3x32x2=0\frac{3 \sqrt{x^{3}}}{2 x^{2}} = 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→−∞(2x3)=∞i\lim_{x \to -\infty}\left(2 \sqrt{x^{3}}\right) = \infty i
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞(2x3)=∞\lim_{x \to \infty}\left(2 \sqrt{x^{3}}\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 2*sqrt(x^3), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(2x3x)=−∞i\lim_{x \to -\infty}\left(\frac{2 \sqrt{x^{3}}}{x}\right) = - \infty i
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
lim⁡x→∞(2x3x)=∞\lim_{x \to \infty}\left(\frac{2 \sqrt{x^{3}}}{x}\right) = \infty
Let's take the limit
so,
inclined asymptote on the right doesn’t exist
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:
2x3=2−x32 \sqrt{x^{3}} = 2 \sqrt{- x^{3}}
- No
2x3=−2−x32 \sqrt{x^{3}} = - 2 \sqrt{- x^{3}}
- No
so, the function
not is
neither even, nor odd
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