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Rutgers University-Camden 640:121 Calculus I Final review questions 1. Use the Intermediate Value Theorem and Rolle's Theorem to prove that the equation 3r + 1 - sin x = 0 has exactly one solution. (Use proof by contradiction following an example we did in class.) 2. Let y = - In r (a) Find all critical points of y. (b) Use the Second Derivative Test to determine any local extrema of this graph. (c) Show that this graph has one point of inflection. 3. Define f(x) = VI on I = [0, 4). (a) Sketch a graph representing the area under f on I, then find / f(x) dx using antideriva- tives. (b) Let ci = - and Ar, = G; - G-1. Evaluate / f(x) dx using the Riemann su these definitions. 4. Let h(x) be the function defined by '+ 2x+1 if -45x