mylearningspace.wlu.ca A-100-Labs - Intro Calc for Natural Science Launch Meeting - Zoom 1 of 2 + Automatic Zoom v all steps in the solutions to the following problems. Insufficient justification will result in a loss of marks. [8 marks] Consider the function f(x) = re-22. (a) Given that f'(x) = -2e-2x (x4 - 2x3), determine the interval(s) on which f is increasing and on which f is decreasing. (b) Given that f"(x) = 4x2e-2(x2 - 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 f has a local extremum at x = 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 x = 0? If so, what is the result of the test? If not, explain why