1. Consider the function below. f(x) = -4x2 + 8x + 1 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) X = (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) increasing decreasing (c) Apply the First Derivative Test to identify the relative extrema. (If an answer does not exist, enter DNE.) relative minimum (x, y) : relative maximum (x, y) :

your work. For the function f(x) -x² + 3x, find each of the following. Show ts.) Average rate of change on the interval [-2, -1]. Average rate of change from x = 1 to x = 3. Name one x interval on which the average rate of change is zero. Domain: (3, 4.5) Graph of f(x) On what interval is the function decreasing? Give the entire interval and use interval notation. What are the domain and range of f(x)? Use interval notation. Range::

You MUST show ALL of your work.  1) Prove the following properties for even and odd functions.  Part A: (Even)(Even)=Even Part B: (Odd)(Odd)=Even Part C: (Even)(Odd)=Odd Part D: (Odd)±(Odd)=Odd Part E: (Even)±(Even)=Even

Find the max, min and intervals of inc/dec of the following function: f(x)=ex/(3x)   [0,10] a. Identify what test you will use b. Use the test correctly c. Write formal sentences for your answer. ***Address all parts of the question.