Find the following for f(x) = \frac{x^{2}+3x}{x−1} = \frac{x(x+3)}{x−1} (if they exist; if they don’t exist, state so). Use this information to graph f. Note f′(x) = \frac{(x−3)(x+1)}{(x−1)^{2}}, f′′(x) = \frac{8}{(x−1)^{3}} [1.5] 1a.) critical numbers: \underline{−1, 3} [1.5] 1b.) local maximum(s) occur at x = \underline{−1} [1.5] 1c.) local minimum(s) occur at x = \underline{−3} [1.5] 1d.) The global maximum of f on the interval [0, 5] is \underline{none} and occurs at x = \underline{none} [1.5] 1e.) The global minimum of f on the interval [0, 5] is \underline{none} and occurs at x = \underline{none} [1.5] 1f.) Inflection point(s) occur at x = \underline{none} [1.5] 1g.) f increasing on the intervals \underline{(−∞, −1) ∪ (3, ∞)} [1.5] 1h.) f decreasing on the intervals \underline{(−1, 1) ∪ (1, 3)} [1.5] 1i.) f is concave up on the intervals \underline{(1, ∞)} [1.5] 1j.) f is concave down on the intervals \underline{(−∞, 1)} [1.5] 1k.) Equation(s) of vertical asymptote(s): \underline{x = 1}

[4] 1l.) Equation(s) of horizontal and/or slant asymptote(s): \underline{y = x + 3} [4.5] 1m.) Graph f