Mixing
Function approximating camels humps?
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I want to construct a function with two maxima and a minima in between that would approximate the two humps of a camel.
In addition, I would like that there would be some effort (not a polynomial) to find the derivatives. And I would also like that the stationary points and inflection points can be evaluated without a calculator.
The closest I got was the function $$ln(8 - frac{1}{4}x^4 + 3 x^2 - 4 x),$$
but the inflection points are not nice.
functions graphing-functions stationary-point
asked Jan 30 at 9:13
Jake B.Jake B.
1786
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add a comment |
$begingroup$
I want to construct a function with two maxima and a minima in between that would approximate the two humps of a camel.
In addition, I would like that there would be some effort (not a polynomial) to find the derivatives. And I would also like that the stationary points and inflection points can be evaluated without a calculator.
The closest I got was the function $$ln(8 - frac{1}{4}x^4 + 3 x^2 - 4 x),$$
but the inflection points are not nice.
functions graphing-functions stationary-point
asked Jan 30 at 9:13
Jake B.Jake B.
1786
$endgroup$
$begingroup$
I think tasks like this are closer to art than mathematics. It's an artform, choosing the correct functions and coefficients.
$endgroup$
– Matti P.
Jan 30 at 9:15
$begingroup$
Well, I'm not trying to get the real-life curve, I just want to create an exercise.
$endgroup$
– Jake B.
Jan 30 at 14:07
add a comment |
$begingroup$
I want to construct a function with two maxima and a minima in between that would approximate the two humps of a camel.
In addition, I would like that there would be some effort (not a polynomial) to find the derivatives. And I would also like that the stationary points and inflection points can be evaluated without a calculator.
The closest I got was the function $$ln(8 - frac{1}{4}x^4 + 3 x^2 - 4 x),$$
but the inflection points are not nice.
functions graphing-functions stationary-point
asked Jan 30 at 9:13
Jake B.Jake B.
1786
$endgroup$
I want to construct a function with two maxima and a minima in between that would approximate the two humps of a camel.
In addition, I would like that there would be some effort (not a polynomial) to find the derivatives. And I would also like that the stationary points and inflection points can be evaluated without a calculator.
The closest I got was the function $$ln(8 - frac{1}{4}x^4 + 3 x^2 - 4 x),$$
but the inflection points are not nice.
functions graphing-functions stationary-point
functions graphing-functions stationary-point
asked Jan 30 at 9:13
Jake B.Jake B.
1786
asked Jan 30 at 9:13
Jake B.Jake B.
1786
asked Jan 30 at 9:13
Jake B.Jake B.
1786
asked Jan 30 at 9:13
Jake B.Jake B.
1786
asked Jan 30 at 9:13
Jake B.Jake B.
1786
1786
$begingroup$
I think tasks like this are closer to art than mathematics. It's an artform, choosing the correct functions and coefficients.
$endgroup$
– Matti P.
Jan 30 at 9:15
$begingroup$
Well, I'm not trying to get the real-life curve, I just want to create an exercise.
$endgroup$
– Jake B.
Jan 30 at 14:07
add a comment |
$begingroup$
I think tasks like this are closer to art than mathematics. It's an artform, choosing the correct functions and coefficients.
$endgroup$
– Matti P.
Jan 30 at 9:15
$begingroup$
Well, I'm not trying to get the real-life curve, I just want to create an exercise.
$endgroup$
– Jake B.
Jan 30 at 14:07
$begingroup$
I think tasks like this are closer to art than mathematics. It's an artform, choosing the correct functions and coefficients.
$endgroup$
– Matti P.
Jan 30 at 9:15
$begingroup$
I think tasks like this are closer to art than mathematics. It's an artform, choosing the correct functions and coefficients.
$endgroup$
– Matti P.
Jan 30 at 9:15
$begingroup$
Well, I'm not trying to get the real-life curve, I just want to create an exercise.
$endgroup$
– Jake B.
Jan 30 at 14:07
$begingroup$
Well, I'm not trying to get the real-life curve, I just want to create an exercise.
$endgroup$
– Jake B.
Jan 30 at 14:07
add a comment |
1 Answer
1
active
oldest
votes
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How about this function? $$f(x)=2e^{-x^2}+2e^{-(x-2)^2}-e^{-(x-1)^2}$$
Its graph looks like this:
answered Feb 22 at 23:05
Robert HowardRobert Howard
2,2933935
$endgroup$
1
$begingroup$
Good idea to use normal distributions!
$endgroup$
– Jake B.
Feb 24 at 17:51
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
How about this function? $$f(x)=2e^{-x^2}+2e^{-(x-2)^2}-e^{-(x-1)^2}$$
Its graph looks like this:
answered Feb 22 at 23:05
Robert HowardRobert Howard
2,2933935
$endgroup$
1
$begingroup$
Good idea to use normal distributions!
$endgroup$
– Jake B.
Feb 24 at 17:51
add a comment |
$begingroup$
How about this function? $$f(x)=2e^{-x^2}+2e^{-(x-2)^2}-e^{-(x-1)^2}$$
Its graph looks like this:
answered Feb 22 at 23:05
Robert HowardRobert Howard
2,2933935
$endgroup$
1
$begingroup$
Good idea to use normal distributions!
$endgroup$
– Jake B.
Feb 24 at 17:51
add a comment |
$begingroup$
How about this function? $$f(x)=2e^{-x^2}+2e^{-(x-2)^2}-e^{-(x-1)^2}$$
Its graph looks like this:
answered Feb 22 at 23:05
Robert HowardRobert Howard
2,2933935
$endgroup$
How about this function? $$f(x)=2e^{-x^2}+2e^{-(x-2)^2}-e^{-(x-1)^2}$$
Its graph looks like this:
answered Feb 22 at 23:05
Robert HowardRobert Howard
2,2933935
answered Feb 22 at 23:05
Robert HowardRobert Howard
2,2933935
answered Feb 22 at 23:05
Robert HowardRobert Howard
2,2933935
answered Feb 22 at 23:05
Robert HowardRobert Howard
2,2933935
2,2933935
1
$begingroup$
Good idea to use normal distributions!
$endgroup$
– Jake B.
Feb 24 at 17:51
add a comment |
1
$begingroup$
Good idea to use normal distributions!
$endgroup$
– Jake B.
Feb 24 at 17:51
1
1
$begingroup$
Good idea to use normal distributions!
$endgroup$
– Jake B.
Feb 24 at 17:51
$begingroup$
Good idea to use normal distributions!
$endgroup$
– Jake B.
Feb 24 at 17:51
add a comment |
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$begingroup$
I think tasks like this are closer to art than mathematics. It's an artform, choosing the correct functions and coefficients.
$endgroup$
– Matti P.
Jan 30 at 9:15
$begingroup$
Well, I'm not trying to get the real-life curve, I just want to create an exercise.
$endgroup$
– Jake B.
Jan 30 at 14:07