1. Let f (x) = ex/ 1+ex (a) Find the derivative f'. Carefully justify each step...

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1. Let f (x) = ex/ 1+ex (a) Find the derivative f'. Carefully justify each step using the differentiation rules from the text. (You may identify rules by the number or by a short description such as the quotient rule.) (b) Find the interval(s) where f '(x) > 0 or f '(x) < 0. (c) Find limx→∞of (x) and limx→→∞of (x). (d) Use the information above to sketch the graph of f. 2. (a) Write an equation for tangent line at a point (a, a2) on the graph of y = x2. (b) Find an equation that a must satisfy if the tangent lines passes through the point (-1/2,-2). (c) Solve the equation from part b) and find all tangent lines to the graph of y = x2 that pass through the point (-1/2, -2). (d) Graph the curve y = x2and the two tangent lines to check your answer. 1. Let f (x) = ex/ 1+ex (a) Find the derivative f'. Carefully justify each step using the differentiation rules from the text. (You may identify rules by the number or by a short description such as the quotient rule.) (b) Find the interval(s) where f '(x) > 0 or f '(x) < 0. (c) Find limx→∞of (x) and limx→→∞of (x). (d) Use the information above to sketch the graph of f. 2. (a) Write an equation for tangent line at a point (a, a2) on the graph of y = x2. (b) Find an equation that a must satisfy if the tangent lines passes through the point (-1/2,-2). (c) Solve the equation from part b) and find all tangent lines to the graph of y = x2 that pass through the point (-1/2, -2). (d) Graph the curve y = x2and the two tangent lines to check your answer.