HW 8 MTH 1410 Name What Derivatives Tell Us Note that this homework has a front and a back. Warning: Be vary careful to note when a question is asking about the original function, the first derivative, or the second derivative. 1. The function f is a continuous function. The graph below is the graph of y = f'(2)- For each part, answer the question and state what characteristic of the graph of y = f'(x) tells you the answer. y = f(x) (a) On what interval(s) is f increasing? (b) At what r-value(s) does f have a local maximum? (c) At what r-value(s) does f have an inflection point? 2. The function g is a continuous function. The graph below is the graph of y = g"(x). In part (a) and (b), answer the question and state what characteristic of the graph of y = g"(x) tells you the answer. 1 =9"(x) (a) On what interval(s) is g concave up? (b) At what r-value(s) does g have an inflection point? (c) Use information from the graph of y = g"(x) to sketch a graph of y = g"(x) on the axes below. y =g"(x)