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(1) The tangent line to y = f(x) at (8, 1) passes through (0, 2). Find f(8), f 0 (8), and the equation of this tangent line.

(2) Sketch the graph of a function that satisfies all of the following conditions.

lim x f(x) = 1 limx f(x) = 5 lim x3 f(x) =

lim x3 f(x) = lim x3+ f(x) = 6 f is continuous from the right at 3

(3) Show that the graph of the function f(x) = 3x^5 + 5x^3 + x 1 crosses the x-axis at some point between x = 0 and x = 1.