Show your work, introduce notation properly (e.g., let r = .. . and y = ...), etc. 2. (5 points) Find all values of c E R so that f(x) = cr - e has a local maximum at a point whose (r and y) coordinates are both positive. Justify your answer (e.g., by applying Fermat's theorem or the first derivative test). 3 (5 points) at be a different15 PUbel 4. (5 points) Compute the following limits and show how you obtained your answer. (a) lim (e +2)/ , where k > 0 is a real constant. (b) lim 5 - 24+ 23 -2+1 2-1 ' - 1023 + 20x2 - 15x + 4