I need help with this word problem please

Step-by-step explanation:

Given function is,

f(x) =

We can rewrite this function as,

f(x) =

a). Domain of the function is [0, ∞)

Derivative of the function in this domain,

f'(x) =

     =

Since, f'(x) > 0 in the interval [0, ∞)

Function is increasing in the interval [0, ∞)

b). For local maxima and local minima,

  Second derivative of the function,

  f"(x) =

         =  > 0

   So the function should have a local minima.

   But the function is continuous in the interval x ≥ 0,

   There is no local minima (only absolute minima).

c). Since, second derivative is undefined at x = 0,

   There are no inflection points.

d). Since, f"(x) > 0 in the interval [0, ∞)

   Concavity of the curve is UPWARDS.

it has to be a.