The image below is for question 1.

lutions to the following problems. Insufficient justification will result in a loss of marks. 1. [S marks] Consider the function f (3) - ze 2. (a) Given that f'(z) =-2e-2"(x* - 2x3), determine the interval(s) on which f is increasing and on which f is decreasing. (b) Given that {"(x) = Are-25(13 - 4x + 3), determine the intervals on which f is concave up and on which f is concave down. (c) Can the Ist Derivative Test be used to determine whether / has a local extremum at r - 0? If so, what is the result of the test? If not, explain why. (d) Can the 2nd Derivative Test be used to determine whether f has a local extremum at I - 0? If so, what is the result of the test? If not, explain why