Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x) = (4 - x)x^-3 for x > 0. (a) Find the t-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither for the function f. Justify your answer. (b) Find all intervals on which the graph of f is concave down. Justify your answer. (c) Given that f(1) = 2, determine the function f.
