Below is the graph polynomial function f with real coefficie

Below is the graph polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph. (a) The function f is decreasing over which intervals? Choose all that apply. (-infinity, 3) (3, 5) (5, 7) (3, 7) (7, infinity) (b) The function f has local minima at which x-values? If there is more than one value, separate them with commas. (c) What is the sign of the leading coefficient of f? (d) Which of the following is a possibility for the degree of f? Choose all that apply. 4 5 6 7 8 9

Solution

a) Function is decreasing for (-infinity,3) and (5,7)

b) Local Minima (3,7)

c) positive

d) we have 2 minima and 1 local maxima i.e. df/dx = 0 for 3 points

So possible degree for f are 4 ,6,8 (in case of non distint roots)