Name 4. Use the zoom or window settings to look at the graph near each critical number and determine from the Assignment 3 Show all work graph whether each critical number is a local maximum, local minimum, or neither. List them below. Due April 13, 2022 10 points critical number local max, local min, or neither You may discuss the homework and even work together, but please do your own calculations so that you understand; do not just copy what someone else has done. 1. Use your calculator to graph the function f(x)=x-15x* -(1/3)x +6x7 in the standard window (that is, [-10,10] for both x and y) and sketch the graph below. 2. Based on your knowledge of polynomials, do you think this graph shows all local maximum and minimum points of the function? Explain why or why not. 5. a) Do you think there is a single window on the calculator that will show all local maximum and minimum points clearly? b) Sketch a graph of the function that does show all local maximum and minimum points clearly, not necessarily to scale, but labeling maximum and minimum points with exact x-values and approximate y-values. Use calculus to solve for exact values of all critical numbers. Hint: The derivative can be factored, with each factor having degree 1 or 2; remember the technique of factoring by grouping, as in the following example. 2x +5x -6x-15=x(2x+5)-3(2x+5)= (x -3)2x+5) (please turn over)