33. 1 Suppose that the function f has a continuous second derivative for all x, and...

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33. 1 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 the 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. b.) Is there sufficient information to determine whether or not the graph of f has a point of inflection when x = 0? Explain your answer. 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) - f'(x) + 2f"(x)). 34. 3x+1 Let f be a function with f(1) = 4 such that for all points (x, y) on the graph off the slope is given by 3+1 2y a.) Find the slope of the graph off at the point where x = 1 and use it to write the tangent line to the graph. b.) Use your answer from part (a) to approximate F(1.2). 33. 1 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 the 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. b.) Is there sufficient information to determine whether or not the graph of f has a point of inflection when x = 0? Explain your answer. 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) - f'(x) + 2f"(x)). 34. 3x+1 Let f be a function with f(1) = 4 such that for all points (x, y) on the graph off the slope is given by 3+1 2y a.) Find the slope of the graph off at the point where x = 1 and use it to write the tangent line to the graph. b.) Use your answer from part (a) to approximate F(1.2).