Easiest way to draw function with Euler's Number












0














What is the easiest way to draw a function like this one?$$frac{1}{7}e^{-2x^2}(1-4x^2)$$ I calculated the roots $x=-1/2$, $x=1/2$ and limit which is equal to $0$
I can't just substitute some values like $f(0)approx 0,15$ into the formula and draw it, can I?






graphing-functions







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  • 2




    Take it's derivative, that often gives you a picture of how the function changes.
    – Don Thousand
    2 days ago






  • 1




    The easiest way is to ask Wolfram Alpha, but that's probably not what you really want.
    – Robert Israel
    2 days ago
















0














What is the easiest way to draw a function like this one?$$frac{1}{7}e^{-2x^2}(1-4x^2)$$ I calculated the roots $x=-1/2$, $x=1/2$ and limit which is equal to $0$
I can't just substitute some values like $f(0)approx 0,15$ into the formula and draw it, can I?






graphing-functions







share|cite|improve this question


















  • 2




    Take it's derivative, that often gives you a picture of how the function changes.
    – Don Thousand
    2 days ago






  • 1




    The easiest way is to ask Wolfram Alpha, but that's probably not what you really want.
    – Robert Israel
    2 days ago














0












0








0







What is the easiest way to draw a function like this one?$$frac{1}{7}e^{-2x^2}(1-4x^2)$$ I calculated the roots $x=-1/2$, $x=1/2$ and limit which is equal to $0$
I can't just substitute some values like $f(0)approx 0,15$ into the formula and draw it, can I?






graphing-functions







share|cite|improve this question













What is the easiest way to draw a function like this one?$$frac{1}{7}e^{-2x^2}(1-4x^2)$$ I calculated the roots $x=-1/2$, $x=1/2$ and limit which is equal to $0$
I can't just substitute some values like $f(0)approx 0,15$ into the formula and draw it, can I?






graphing-functions




graphing-functions






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share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 2 days ago









B. Czostek

566




566








  • 2




    Take it's derivative, that often gives you a picture of how the function changes.
    – Don Thousand
    2 days ago






  • 1




    The easiest way is to ask Wolfram Alpha, but that's probably not what you really want.
    – Robert Israel
    2 days ago














  • 2




    Take it's derivative, that often gives you a picture of how the function changes.
    – Don Thousand
    2 days ago






  • 1




    The easiest way is to ask Wolfram Alpha, but that's probably not what you really want.
    – Robert Israel
    2 days ago








2




2




Take it's derivative, that often gives you a picture of how the function changes.
– Don Thousand
2 days ago




Take it's derivative, that often gives you a picture of how the function changes.
– Don Thousand
2 days ago




1




1




The easiest way is to ask Wolfram Alpha, but that's probably not what you really want.
– Robert Israel
2 days ago




The easiest way is to ask Wolfram Alpha, but that's probably not what you really want.
– Robert Israel
2 days ago










1 Answer
1






active

oldest

votes


















3














A good approach is to see what each factor does. The second factor $1 - 4x^2$ is a parabola opening down, and at $x = 0$ reaches its maximum $1$. The first factor takes everything and makes it smaller, unless $x$ is very close to $0$, in which case it just leaves it mostly unchanged.



So in you put these ideas together: you expect a parabola close to the origin, going to zero as $x$ moves away from $0$



enter image description here



A minimal version of the code to produce the graph above in Python



import numpy as np

import matplotlib.pyplot as plt



x = np.linspace(-2, 2, num = 200)

y1 = np.exp(-2 * x**2)

y2 = 1 - 4 * x**2



plt.plot(x, y1)

plt.plot(x, y2)

plt.plot(x, y1 * y2)

plt.show()





share|cite|improve this answer























  • What tools did you use to make that graph?
    – lhf
    2 days ago










  • @lhf Python, I just included the code to create the graph
    – caverac
    2 days ago











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1 Answer
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3














A good approach is to see what each factor does. The second factor $1 - 4x^2$ is a parabola opening down, and at $x = 0$ reaches its maximum $1$. The first factor takes everything and makes it smaller, unless $x$ is very close to $0$, in which case it just leaves it mostly unchanged.



So in you put these ideas together: you expect a parabola close to the origin, going to zero as $x$ moves away from $0$



enter image description here



A minimal version of the code to produce the graph above in Python



import numpy as np

import matplotlib.pyplot as plt



x = np.linspace(-2, 2, num = 200)

y1 = np.exp(-2 * x**2)

y2 = 1 - 4 * x**2



plt.plot(x, y1)

plt.plot(x, y2)

plt.plot(x, y1 * y2)

plt.show()





share|cite|improve this answer























  • What tools did you use to make that graph?
    – lhf
    2 days ago










  • @lhf Python, I just included the code to create the graph
    – caverac
    2 days ago
















3














A good approach is to see what each factor does. The second factor $1 - 4x^2$ is a parabola opening down, and at $x = 0$ reaches its maximum $1$. The first factor takes everything and makes it smaller, unless $x$ is very close to $0$, in which case it just leaves it mostly unchanged.



So in you put these ideas together: you expect a parabola close to the origin, going to zero as $x$ moves away from $0$



enter image description here



A minimal version of the code to produce the graph above in Python



import numpy as np

import matplotlib.pyplot as plt



x = np.linspace(-2, 2, num = 200)

y1 = np.exp(-2 * x**2)

y2 = 1 - 4 * x**2



plt.plot(x, y1)

plt.plot(x, y2)

plt.plot(x, y1 * y2)

plt.show()





share|cite|improve this answer























  • What tools did you use to make that graph?
    – lhf
    2 days ago










  • @lhf Python, I just included the code to create the graph
    – caverac
    2 days ago














3












3








3






A good approach is to see what each factor does. The second factor $1 - 4x^2$ is a parabola opening down, and at $x = 0$ reaches its maximum $1$. The first factor takes everything and makes it smaller, unless $x$ is very close to $0$, in which case it just leaves it mostly unchanged.



So in you put these ideas together: you expect a parabola close to the origin, going to zero as $x$ moves away from $0$



enter image description here



A minimal version of the code to produce the graph above in Python



import numpy as np

import matplotlib.pyplot as plt



x = np.linspace(-2, 2, num = 200)

y1 = np.exp(-2 * x**2)

y2 = 1 - 4 * x**2



plt.plot(x, y1)

plt.plot(x, y2)

plt.plot(x, y1 * y2)

plt.show()





share|cite|improve this answer














A good approach is to see what each factor does. The second factor $1 - 4x^2$ is a parabola opening down, and at $x = 0$ reaches its maximum $1$. The first factor takes everything and makes it smaller, unless $x$ is very close to $0$, in which case it just leaves it mostly unchanged.



So in you put these ideas together: you expect a parabola close to the origin, going to zero as $x$ moves away from $0$



enter image description here



A minimal version of the code to produce the graph above in Python



import numpy as np

import matplotlib.pyplot as plt



x = np.linspace(-2, 2, num = 200)

y1 = np.exp(-2 * x**2)

y2 = 1 - 4 * x**2



plt.plot(x, y1)

plt.plot(x, y2)

plt.plot(x, y1 * y2)

plt.show()






share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 2 days ago

























answered 2 days ago









caverac

13.8k21130




13.8k21130












  • What tools did you use to make that graph?
    – lhf
    2 days ago










  • @lhf Python, I just included the code to create the graph
    – caverac
    2 days ago


















  • What tools did you use to make that graph?
    – lhf
    2 days ago










  • @lhf Python, I just included the code to create the graph
    – caverac
    2 days ago
















What tools did you use to make that graph?
– lhf
2 days ago




What tools did you use to make that graph?
– lhf
2 days ago












@lhf Python, I just included the code to create the graph
– caverac
2 days ago




@lhf Python, I just included the code to create the graph
– caverac
2 days ago


















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