1. Let f(x) = 3x- 8x3- 90x2 (1). (1 points) Find f"(x), the second derivative of f. (ii) . (3 points) Find the interval(s) in which f is concave down. Justify your answer with the appropriate sign chart, or by other means that do not rely on a graphing calculator/app/website. 2. (5 points) A certain function G is continuous at all real numbers. The graph of its derivative G' is shown below. In which interval(s) is the original function G concave up? [No participation points will be given if t the questions are answered as if the graph is that of the original function.] -5 5 3. (6 points) Find the interval in which the function g(x) = xe" is concave down. Justify your answer with the appropriate sign chart, or by other means that do not rely on a graphing calculator/app/website. [You found the factored form of the second derivative in an earlier recitation. The correct answer is g" (x) = 3x (x - 2)(3x - 2)e-3x . ] Available after Oct 13, 2021 12:00am Details 1. (3 points) Let f(x) = 3x4 - 8x3 - 90x2 Classify the critical values of f into relative maxima, relative minima, and neither using the second derivative test. [no credit will be given without relevant work, or if a different method is used.] [Recall from an earlier recitation that the critical values of this function are -3, 0, and 5.]