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I have been trying to create a function with given local extrema and an extra parameter with no luck.

enter image description here

So as you can see in the image I need a function with local minimum at C with value -C and local maximum at -C with value C. It is also important that the function goes through the (-D,-D) and (D,D) points. Note that D is always grater then C. C and D are free parameters here. It is also important the function is differentiable and continuous.

I have been trying to create a polynomial with such a parameters with no luck. Could somebody help me out here?

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    Try to integrate $f'(x)=K(x+C)(x-C)$ and find appropriate constant $K$ so that the function satisfies $f(\pm D)=\pm D$? – 2017-02-15
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    $K=\frac{3}{D^2-3C^2}$ works with the method I mentioned above as long as $D^2\neq 3C^2$ – 2017-02-15
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    Thanks for the quich response. So what I have now then is f(x)= (((3/(D^2-3*C^2))*(x^3-3C^2x))/3)+C . Is this right? cause It doesn't seem to give me a good result. Sorry I don't know how to make the equation fancy :( – 2017-02-15
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    With the choice of $K$ I mentioned the end result should be $f(x)=\frac{x^3}{D^2-3C^2}-\frac{3C^2}{D^2-3C^2}x$. You don't want any constant term as you want them to pass through origin – 2017-02-15
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    So I tried the f(x)=x3D2−3C2−3C2D2−3C2x with D = 3 and C = 0.5. It has local min/max at -0.5 and 0.5 but its value at 0.5 and -0.5 are not -0.5 and 0.5 – 2017-02-15
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    Let $ \lambda y = x ( x^2-4)$ by antisymmetry and we have for max/min $ x= C= 2/\sqrt3$ by differentiation. One equation is $ \lambda C= \pm 16/(3 \sqrt3)$, another $ D^2-4 = \lambda$ – 2017-02-15
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    I don't think you have your function correct, that's not in the form I suggested. Besides you want it to take $\pm 3$ at $\pm 3$, not the one you described. You said you want to take $\pm D$ to $\pm D$ not $\pm C$ to $\pm C$ – 2017-02-15
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    user160738 - If you look at the image I provided I want the local maximum and minimum at -C and C respectively with value C and -C. and In addition I want the constraint with the D – 2017-02-15
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    Narasimham - How should I plot your function? – 2017-02-15

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