Question 1. In this question you will be exploring the shape of the family of graphs:...

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Question 1. In this question you will be exploring the shape of the family of graphs: (x) = Kx + x + x where K is a real parameter. In particular, you will discover how K affects the local extrema and critical points of f. (5) There is only one K value where f has a absolute min. Find it! (6) Complete the following sentences (with justification) with the entire collection of Ks with these properties. (In the case there are no such K, then say "none".) When K is then f has 0 critical points. When K is When K is When K is then f has exactly 1 critical point. then f has exactly 2 critical points. then f has 3 or more critical point. Question 1. In this question you will be exploring the shape of the family of graphs: (x) = Kx + x + x where K is a real parameter. In particular, you will discover how K affects the local extrema and critical points of f. (5) There is only one K value where f has a absolute min. Find it! (6) Complete the following sentences (with justification) with the entire collection of Ks with these properties. (In the case there are no such K, then say "none".) When K is then f has 0 critical points. When K is When K is When K is then f has exactly 1 critical point. then f has exactly 2 critical points. then f has 3 or more critical point.