1 Calculus Question

For each of the following problems you will be creating a sketch for the graph ofthe given function by following steps (a), (b), and (c), and then using the information you gathered in these steps to create your graph. (Your information from (a) to (c) should be clearly seen in your sketch and this is how the marks for (d) will be assigned. If your information does not match your sketch, then that indicates there are issues with either that information or with your sketch.) 1. f(x) = 4x5/2 8x3/2 Domain: [0, 00) a. Compute f'(x) and f"(x). (Simplify your answers.) [4 marks] b. Use f'(x) to determine where f(x) is increasing and where f(x) is decreasing and find each local maximum/minimum (give the coordinates (x, y) of each points). [2 marks] c. Use f"(x) to determine where f(x) is concave upwards and where f(x) is concave downward. Find the coordinates (x, y) of each inflection point. [2 marks] d. Find any x- or y- intercepts and then sketch the curve using the information collected from (a) to (c). [2 marks]