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3*sqrt(x)/2

  • How to use it?

  • Graphing y =:
  • (x^2+5)/(x-3)
  • -6x^2+x+1
  • 2x^3-3x^2+5
  • x^4-2x^2-8

  • Identical expressions

  • three *sqrt(x)/ two
  • 3 multiply by square root of (x) divide by 2
  • three multiply by square root of (x) divide by two
  • 3*√(x)/2
  • 3sqrt(x)/2
  • 3sqrtx/2
  • 3*sqrt(x) divide by 2
Plotting a function graph/ 3*sqrt(x)/2

Graphing y = 3*sqrt(x)/2

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The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
           ___
       3*\/ x 
f(x) = -------
          2
f(x)=3x2f{\left(x \right)} = \frac{3 \sqrt{x}}{2} 
f = 3*sqrt(x)/2
The graph of the function
02468-8-6-4-2-101005
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:
3x2=0\frac{3 \sqrt{x}}{2} = 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 3*sqrt(x)/2.
302\frac{3 \sqrt{0}}{2}
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
34x=0\frac{3}{4 \sqrt{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
−38x32=0- \frac{3}{8 x^{\frac{3}{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→−∞(3x2)=∞i\lim_{x \to -\infty}\left(\frac{3 \sqrt{x}}{2}\right) = \infty i
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞(3x2)=∞\lim_{x \to \infty}\left(\frac{3 \sqrt{x}}{2}\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 3*sqrt(x)/2, divided by x at x->+oo and x ->-oo
lim⁡x→−∞(32x)=0\lim_{x \to -\infty}\left(\frac{3}{2 \sqrt{x}}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(32x)=0\lim_{x \to \infty}\left(\frac{3}{2 \sqrt{x}}\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:
3x2=3−x2\frac{3 \sqrt{x}}{2} = \frac{3 \sqrt{- x}}{2}
- No
3x2=−3−x2\frac{3 \sqrt{x}}{2} = - \frac{3 \sqrt{- x}}{2}
- No
so, the function
not is
neither even, nor odd
The graph
Graphing y = 3*sqrt(x)/2
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