Back

Workouts- Shape of Functions

1.1

When is \(\left(\frac{1}{x}+\frac{1}{y}\right)^\alpha\) quasiconcave on \((x,y)\in\mathbb{R}^2_{>0}\)?

1.2

Prove \(\left(1+\frac{1}{x}\right)^{x}\) is monotone on \(x\in\mathbb{R}_{>0}\).

1.3

Prove \(\prod_i^n\left(x_i^{\alpha_i}\right)\) is quasiconcave.