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Transcript
AP Calculus BC ___________________ 1. FR: FTC Practice Name: 11-18-15 Let f be a differentiable function, defined for all real numbers x, with the following properties. (ii) f (x) ax 2 bx f (1) 6 and f (1) 18 (iii) (i) 2 1 f (x)dx 18 Find f (x) . Show your work. 2. Let f be a function such that f (x) 6x 8 . (a) Find f (x) if the graph of f is tangent to the line 3x y 2 at the point (0, -2). (b) 3. Find the average value of f (x) on the closed interval [-1, 1]. Let f be the function that is defined for all real numbers x and that has the following properties. (i) (ii) (iii) (a) f (x) 24x 18 f (1) 6 f (2) 0 Find each x such that the line tangent to the graph of f at (x, f (x)) is horizontal. (b) (c) 4. Write an expression for f (x) . Find the average value of f on the interval 1 x 3 . Let f and g be continuous functions with the following properties. (i) g(x) A f (x) where A is a constant (ii) 2 (iii) 3 1 2 3 f (x)dx 3 2 g(x)dx f (x)dx 3A (a) Find (b) Find the average value of g(x) in terms of A over the interval [1, 3]. 1 f (x)dx in terms of A. (c) Find the value of k if 1 0 f (x 1)dx kA .