Mister Exam
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-
How to use it?
- Graphing y =:
- (x-1)/(x+5)
- x^3-3x^2-9x+10
- x³-2x
- x^3-27x
- Derivative of:
-
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
Graphing y = 2*sqrt(x^3)
The solution
You have entered
[src]
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f(x) = 2*\/ x
$$f{\left(x \right)} = 2 \sqrt{x^{3}}$$
f = 2*sqrt(x^3)
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:
$$2 \sqrt{x^{3}} = 0$$
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:
$$2 \sqrt{x^{3}} = 0$$
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
$$\frac{3 \sqrt{x^{3}}}{x} = 0$$
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
$$\frac{3 \sqrt{x^{3}}}{x} = 0$$
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
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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
$$\frac{3 \sqrt{x^{3}}}{2 x^{2}} = 0$$
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
$$\frac{3 \sqrt{x^{3}}}{2 x^{2}} = 0$$
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
$$\lim_{x \to -\infty}\left(2 \sqrt{x^{3}}\right) = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(2 \sqrt{x^{3}}\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(2 \sqrt{x^{3}}\right) = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(2 \sqrt{x^{3}}\right) = \infty$$
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
$$\lim_{x \to -\infty}\left(\frac{2 \sqrt{x^{3}}}{x}\right) = - \infty i$$
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{2 \sqrt{x^{3}}}{x}\right) = \infty$$
Let's take the limit
so,
inclined asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(\frac{2 \sqrt{x^{3}}}{x}\right) = - \infty i$$
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{2 \sqrt{x^{3}}}{x}\right) = \infty$$
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:
$$2 \sqrt{x^{3}} = 2 \sqrt{- x^{3}}$$
- No
$$2 \sqrt{x^{3}} = - 2 \sqrt{- x^{3}}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$2 \sqrt{x^{3}} = 2 \sqrt{- x^{3}}$$
- No
$$2 \sqrt{x^{3}} = - 2 \sqrt{- x^{3}}$$
- No
so, the function
not is
neither even, nor odd