2. [5 points} Find all values of c E R so that {(13) : co: er has a local maximum at. a point whose (1: and y) coordinates are both positive. Justify your answer [e.g.. by applying Fermat's theorem or the rst derivative test}. 3. [5 points} Let f be a differentiable function 011R with {(1) = 7' and {{4} = 1. Furthermore. suppose that there is a value of l: E R such that Iii-T} if. A: for all I. (i) Is it possible that k = 5'E' (ii) Is it possible that F: = 2? (iii) ls it possible that I: = 7r? Justify each answer {e.g.. by applying the Mean Value Theorem or giving an example showing it is possible}. 4. (5 points}I Compute the following limits and show how you obtained your answer. (a) lim (e1 + If". where I: :1} {l is a real constant. (b) Hm 1-5 1-4 + r3 212 + 1 Lit)1 .175 1UI3 + in'?' 15.1: + 11