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Question 1. In this question you will be exploring the shape of the family of graphs: fk(x) = Ka' + x2+ 2 where K is a real parameter. In particular, you will discover how K affects the local extrema and critical points of fK. You use this Desmos graph: https ://www. desmos. com/calculatora2gw9wahd (1) Warmup. Play around with the graph on Desmos and try many different values of K. . What do you notice? . Are there any special/interesting values of K where something spe cial/interesting happens? . What do you wonder? . Can you make fx have 2 critical points? 1 critical point only? 0 critical points? . Does fx ever have an absolute max or absolute min? [You do not need to submit anything for this part.] (2) Show that f1 (i.e. K = 1) is always increasing, and has no critical points.(5) There is only one K value where fx has a absolute min. Find it! (4) There is only one K value where fx has a critical point that is neither a local max or local min. Find it! (6) Complete the following sentences (with justification) with the entire collection of K's with these properties. (In the case there are no such K, then say \"none\".) e When K is e When K is e When K is e When K is then fg has 0 critical points. then fx has exactly 1 critical point. then fx has exactly 2 critical points. then fx has 3 or more critical point. (3) Show that if K = -, then fx has two critical points. Find them, and classify them (i.e. are they local maxs, local mins, or neither)