I have the following function:
f[y_] = y (k + h (1 - y - x) - t (1 - y - x) x + (1 - y) t (-y + x))
where k, h and t are parameters with values comprehended in the interval [0,1]. I already studied its concavity computing the second derivative wrt to y and using Reduce in order to understand when it is negative.
foc = D[f[y], y] soc = D[foc, y] Reduce[soc < 0]
Which gives the following output:
x \[Element] Reals && (t | y) \[Element] Reals && h > -t + 3 t y
I interpreted it as "the function is concave when
h > -t + 3 t y (I do not understand the other part of the output).
Now, I would like to study under which conditions the function is quasi-concave. How can I do it?