Suppose that the production function is $f(x_1,x_2)=C{x}_1^a{x}_2^b,$ where $a,b,$ and $C$ are positive constants.

$($a$)$ For what positive values of $a,b,$ and $C$ are there decreasing returns to scale? constant returns to scale?

increasing returns to scale?

$($b$)$ For what positive values of $a,b,$ and $C$ is there decreasing marginal product for factor $1?$

$)$

$($c$)$ For what positive values of $a,b,$ and $C$ is there diminishing technical rate of substitution?