Prove that a quasiconcave function cannot have a strict mini

Prove that a quasiconcave function cannot have a strict minimum at any interior point on its domain.

Solution

If we plot a Qusi concave function on a graph ,it looks like a badly built bowl. the graph shows some bumps and so the function is generally concave but not perfectly concave. concavity is thus just an instance of quasi cocave function. But it still have a depression in the centre and two ends that tilt upwards.

The minimum of the function should lie in the above mentioned depression. Consider the depression alone and it look more or less like a continuous straight line and a strict minimum in between that straight line is not possible.