Let f : IR -> R be the function defined by f(x) =314 -823 - 210x2 + c, where c is some real constant. (a) What are the stationary points of f? Enter your answer as a set. Syntax advice: Enter your set using Maple syntax for sets. For example, the set {0, 1} may be written as {0 , 1} (b) Which of the following intervals is the range of f? O [c - 2375, 00) 0 [c, 00) O [c - 9287, 00) O [c - 5831, 00) O (-00, c] OR O [c - 5831, c - 2375] (c) Let g be the function f restricted to the domain (11, co). Briefly explain in words why g has a differentiable inverse Essay box advice: In your explanation, you don't need to use exact Maple syntax or use the equation editor, as long as your expressions are sufficiently clear for the reader. For example, you can write . f and gas 'f and 'g', respectively, . (11, oo) as '(11, infinity)'. 50 Equation A- A-IX BIUSXX Styles Font Size Words: 0 A Find the exact value of (g 1)' (9(15)) = Note: Enter your answer above as an exact value with correct Maple syntax.(d) On which of the following other intervals does f have an inverse? [Select all that apply.] Multiple selection advice: In a multiple selection question, marks are deducted for incorrect selections (but you cannot get less than zero for it). You are advised to only select options that you are sure about. 0 0, 7 O (-00, -9] O [-5, 7] 0 [0,00) D (-00, 7] (e) Which of the following statements are true about f : K -> R? [Select all that apply.] O For all y E Range(f), the equation y = f(x) has at least 2 solutions. [ For some y E Range(f), the equation y = f(x) has exactly 2 solutions. [ For some y E Range(f), the equation y = f(x) has exactly 3 solutions. O For all y E Range(f), the equation y = f(x) has either 2 or 4 solutions. O For all y E Range( f), the equation y = f(x) has at most 4 solutions. [ For some y E Range( f), the equation y = f() has no solutions. There exist no y c Range(f) such that y = f(x) has fewer than 2 solutions. O For all y E Range(f), the equation y = f(x) has at most 2 solutions