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**Blue Griffin** 2. Suppose that the function f has a continuous second derivative for all x, and that f(0) = 2, f ‘ (0) = -3, and f “ (0) = 0. Let g be a function whose derivative is given by g'(x) = e^-2x(3f(x) + 2f'(x)) for all x.

(a) Write an equation of the line tangent to the graph of f at the point where x = 0.

(c) Given that g(0) = 4, write an equation of the line tangent to the graph of g at the point where x = 0.

(d) Show that g''(x) = e^-2x(-6f(x) 2f''(x)) At x = 0, is g ‘ (x) = 0 and g “ (x) < 0? Justify your answer.