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.

Question

A. Find the x-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 in which the graph of f is concave down. Justify your answer.

C. Given that f(1)=2, determine the function of f.

A- I know for max and min you use first derivative and equal the function to 0 for critical numbers.

B-I know concave down is determined from the second derivative.

C-Do not have any idea how to do it

Thanks for your help

Answer 1

http://apcentral.collegeboard.com/apc/public/repository/ap11_calc_ab_form_b_q4.pdf