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e^(3*x)
  • How to use it?

  • Graphing y =:
  • x^2-9
  • 6x^2
  • 2^x
  • 2sinx 2sinx
  • Derivative of:
  • e^(3*x) e^(3*x)
  • Integral of d{x}:
  • e^(3*x) e^(3*x)
  • Limit of the function:
  • e^(3*x) e^(3*x)
  • Identical expressions

  • e^(three *x)
  • e to the power of (3 multiply by x)
  • e to the power of (three multiply by x)
  • e(3*x)
  • e3*x
  • e^(3x)
  • e(3x)
  • e3x
  • e^3x

Graphing y = e^(3*x)

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The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src]
        3*x
f(x) = e   
f(x)=e3xf{\left(x \right)} = e^{3 x}
f = E^(3*x)
The graph of the function
-0.4-0.20.00.20.40.60.81.01.21.40100
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:
e3x=0e^{3 x} = 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 E^(3*x).
e30e^{3 \cdot 0}
The result:
f(0)=1f{\left(0 \right)} = 1
The point:
(0, 1)
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
3e3x=03 e^{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
9e3x=09 e^{3 x} = 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
limxe3x=0\lim_{x \to -\infty} e^{3 x} = 0
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=0y = 0
limxe3x=\lim_{x \to \infty} e^{3 x} = \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 E^(3*x), divided by x at x->+oo and x ->-oo
limx(e3xx)=0\lim_{x \to -\infty}\left(\frac{e^{3 x}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
limx(e3xx)=\lim_{x \to \infty}\left(\frac{e^{3 x}}{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:
e3x=e3xe^{3 x} = e^{- 3 x}
- No
e3x=e3xe^{3 x} = - e^{- 3 x}
- No
so, the function
not is
neither even, nor odd
The graph
Graphing y = e^(3*x)