Reference no: EM131386342

1. For the following function:y = h(x) = a ln(x + b), for x ≥ 0, determine the possible values of paramaters a and b such that the function takesa value of zero when x = 0 and is always strictly increasing in x.

2. For the following function:y = f(x) = γxθ, for all x ≥ 0 and where γ > 0,determine the possible values of parameter θ such that the function is strictlyincreasing in x, but at an ever-decreasing rate (hint: Take the first and secondderivatives and force the first to be strictly positive. That will give you acondition on the possible values of θ, knowing that x and γ are positive. Thenforce the second derivative to be negative. That will give you a second conditionon the possible values of θ).

3. For γ = 1, graph the function f(x) for the following values of θ:14,12, 1, 2.