Inquiry 4 - Derivatives and the Shape of Graphs When analyzing the graph of function using the first and second derivative tests, we identify the following: The domain and the type of function [even. odd, periodic, asymptotes, behavior at too. ... ] The zeros of f (x-intercepts) [set f (x) = 0 and solve] and y-intercept [ set x = 0] The critical numbers of f [set f'(x) = 0 and solve] The critical points [plug the critical numbers into f (x)] The local min/max [plug the critical numbers into f"(x)] The inflection point(s) of f [set f"(x) = 0 and solve, plug the solutions into f (x)] The intervals of increase/decrease The intervals of concavity Extra points in the graph as needed and sketch the graph as accurately as possible. Follow the above steps to structure your solutions for questions below. 1. Use the first and second derivative tests 101 to analyze the graph of the function f (x) given the graph of its derivative f(x). Sketch the graph of f (x) given that f (0) = 2. P(x) 2 -5 -4 -3 1 6 3 4 5 X - 8 -10CALCULUS I Dr G 2. Use the first and second derivative tests to analyze the function f (x ) given its graph. Sketch the graph of f (x). 10 -43 -10-3. Analyze the function f(x) = x* - 2x7 - 3 using the first and second derivative tests, Sketch the graph of f (x) as accurately as possible. 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6