Calculus Test Question

6. Consider the function f (x) = V3 tan-1 (4x2) a. [2 marks] Show that the derivative, when simplified, is given by f' (x ) = 2x () - 2x 1 1 + 1 + 3 x 4 b. From the given expression for f'(x), determine where the function f (x) is increasing/decreasing, and classify any critical points as local maxima or minima. [2 marks] The function s( x) is increasing Compute and simplify f"(x), then determine where f (x) is concave up / concave down and find the location (x-value) of any inflection points. [4 marks] 5" (x )