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x^(6x-x^2)

  • How to use it?

  • Graphing y =:
  • x^3/2(x+1)^2
  • -x^2+4x-3 -x^2+4x-3
  • x^3+6x^2+9x
  • (x+1)/(x-1)

  • Identical expressions

  • x^(6x-x^ two)
  • x to the power of (6x minus x squared )
  • x to the power of (6x minus x to the power of two)
  • x(6x-x2)
  • x6x-x2
  • x^(6x-x²)
  • x to the power of (6x-x to the power of 2)
  • x^6x-x^2

  • Similar expressions

  • x^(6x+x^2)
Plotting a function graph/ x^(6x-x^2)

Graphing y = x^(6x-x^2)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
               2
        6*x - x 
f(x) = x
f(x)=x−x2+6xf{\left(x \right)} = x^{- x^{2} + 6 x} 
f = x^(-x^2 + 6*x)
The graph of the function
05-50-45-40-35-30-25-20-15-10-51015200100000
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:
x−x2+6x=0x^{- x^{2} + 6 x} = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=−54x_{1} = -54
x2=24.3817230303778x_{2} = 24.3817230303778
x3=22.3991210478115x_{3} = 22.3991210478115
x4=−42x_{4} = -42
x5=−68x_{5} = -68
x6=−94x_{6} = -94
x7=−50x_{7} = -50
x8=64.25x_{8} = 64.25
x9=84.25x_{9} = 84.25
x10=−30.0017403797255x_{10} = -30.0017403797255
x11=66.25x_{11} = 66.25
x12=−92x_{12} = -92
x13=52.25x_{13} = 52.25
x14=72.25x_{14} = 72.25
x15=16.4889704951537x_{15} = 16.4889704951537
x16=−36.0000000003398x_{16} = -36.0000000003398
x17=−88x_{17} = -88
x18=−66x_{18} = -66
x19=−82x_{19} = -82
x20=9.00948551584209x_{20} = 9.00948551584209
x21=50.25x_{21} = 50.25
x22=82.25x_{22} = 82.25
x23=−34.000000086796x_{23} = -34.000000086796
x24=38.25x_{24} = 38.25
x25=−72x_{25} = -72
x26=−58x_{26} = -58
x27=18.4500190992735x_{27} = 18.4500190992735
x28=96.25x_{28} = 96.25
x29=−98x_{29} = -98
x30=58.25x_{30} = 58.25
x31=−52x_{31} = -52
x32=62.25x_{32} = 62.25
x33=30.2547571438968x_{33} = 30.2547571438968
x34=42.25x_{34} = 42.25
x35=60.25x_{35} = 60.25
x36=86.25x_{36} = 86.25
x37=−74x_{37} = -74
x38=−90x_{38} = -90
x39=34.25x_{39} = 34.25
x40=−44x_{40} = -44
x41=76.25x_{41} = 76.25
x42=68.25x_{42} = 68.25
x43=100.25x_{43} = 100.25
x44=90.25x_{44} = 90.25
x45=44.25x_{45} = 44.25
x46=−32.0000206558112x_{46} = -32.0000206558112
x47=−80x_{47} = -80
x48=−86x_{48} = -86
x49=−64x_{49} = -64
x50=36.25x_{50} = 36.25
x51=−84x_{51} = -84
x52=56.25x_{52} = 56.25
x53=28.3561813032928x_{53} = 28.3561813032928
x54=94.25x_{54} = 94.25
x55=−96x_{55} = -96
x56=14.5440547157237x_{56} = 14.5440547157237
x57=12.6267809198562x_{57} = 12.6267809198562
x58=74.25x_{58} = 74.25
x59=−78x_{59} = -78
x60=20.4212017849929x_{60} = 20.4212017849929
x61=92.25x_{61} = 92.25
x62=98.25x_{62} = 98.25
x63=−48x_{63} = -48
x64=−60x_{64} = -60
x65=40.25x_{65} = 40.25
x66=−46x_{66} = -46
x67=78.25x_{67} = 78.25
x68=10.7617462961386x_{68} = 10.7617462961386
x69=−100x_{69} = -100
x70=−56x_{70} = -56
x71=−38.0000000000022x_{71} = -38.0000000000022
x72=−70x_{72} = -70
x73=32.2540232264424x_{73} = 32.2540232264424
x74=48.25x_{74} = 48.25
x75=46.25x_{75} = 46.25
x76=88.25x_{76} = 88.25
x77=−40x_{77} = -40
x78=26.3676995979854x_{78} = 26.3676995979854
x79=−62x_{79} = -62
x80=−76x_{80} = -76
x81=80.25x_{81} = 80.25
x82=54.25x_{82} = 54.25
x83=70.25x_{83} = 70.25
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to x^(6*x - x^2).
06⋅0−020^{6 \cdot 0 - 0^{2}}
The result:
f(0)=1f{\left(0 \right)} = 1
The point:
(0, 1)
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞x−x2+6x=∞\lim_{x \to -\infty} x^{- x^{2} + 6 x} = \infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞x−x2+6x=0\lim_{x \to \infty} x^{- x^{2} + 6 x} = 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 x^(6*x - x^2), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(x−x2+6xx)=∞\lim_{x \to -\infty}\left(\frac{x^{- x^{2} + 6 x}}{x}\right) = \infty
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
lim⁡x→∞(x−x2+6xx)=0\lim_{x \to \infty}\left(\frac{x^{- x^{2} + 6 x}}{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:
x−x2+6x=(−x)−x2−6xx^{- x^{2} + 6 x} = \left(- x\right)^{- x^{2} - 6 x}
- No
x−x2+6x=−(−x)−x2−6xx^{- x^{2} + 6 x} = - \left(- x\right)^{- x^{2} - 6 x}
- No
so, the function
not is
neither even, nor odd
The graph
Graphing y = x^(6x-x^2)
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