Question 1 (10 points) Consider a function f(x) with the following properties • • • • • f(x) is defined and continu- ous everywhere EXCEPT at x = −3. f has a vertical asymptote at x = −3. lim f(x)=2 x→−∞ limf(x)=−4 x→∞ f(x) is continuous but NOT differentiable at x = 5. • f′(x) > 0 on the interval (1, 5). • f′(x) < 0 on the inter- vals (−∞,−3), (−3,1) and (5, ∞). • f′′(x) > 0 on the intervals (−3, 5) and (5, ∞). • f′′(x) < 0 on the interval (−∞, −3). a) (2 point) At what values of x does f have a local maximum (if any)? local minimum (if any)? b) (2 point) What are the x-coordinates of the inflection points of f (if any)? c) (6 points) Draw, on your own axes, a possible graph of a curve y = f(x).