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.
How about this function? $$f(x)=2e^{-x^2}+2e^{-(x-2)^2}-e^{-(x-1)^2}$$
Its graph looks like this: