Question

Show whether the following functions are quasi-concave:
i)f(x)=|x|
ii)g(x)=eˣ

Answer 1

The functions f(x) = |x| and g(x) = e^x are quasi-concave.

Step-by-step explanation:

A function is considered quasi-concave if for any two points in its domain, any point on the line segment connecting the two points lies above the graph of the function.

i) For f(x) = |x|, let's consider two points in its domain, a and b. If we take any point on the line segment connecting a and b, the y-coordinate of that point will always be greater than or equal to the y-coordinate of a and b. This means that f(x) = |x| is quasi-concave.

ii) For g(x) = e^x, let's consider two points in its domain, a and b. If we take any point on the line segment connecting a and b, the y-coordinate of that point will always be greater than or equal to the y-coordinate of a and b. This means that g(x) = e^x is also quasi-concave.