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BC Calculus 1 Sample Quiz Show all appropriate work clearly for full credit. NO CALCULATORS 1. Name: For each function shown below, find its first derivative. DO NOT simplify. e( x 2 x ) f ( x) ln cosh( x) 2 a. f x b. g x tan 1 ( x3 3) sec2 x g x 2. 3. Find f '' x if f ( x) sin x 2 Find values of p and q such that the line y px 5 is tangent to the graph of q x x3 1 at the point where x = 1. x 3a. Suppose h( x) f ( g ( x)) . Given the information about , g and their derivatives provided in the table, fill in the missing information. 2 x 1 2 4 f x 3 –1 5 f x –1 8 6 g ( x) 4 2 1 g ( x) 1 4 3 h( x ) h( x ) 3b. Given the information above, suppose that k ( x) f ( g ( x)) where k is one-to-one and d k 1 ( x ) at x = 5. differentiable. Evaluate the dx ln( x) 1 . Determine the exact value of x for which this function has a stationary x point, then determine whether k has a local max, a local min, or neither at this point. Be sure to justify. Let k x 4. 5. Consider the curve defined by the equation 3 y3 12 x2 y 16 x3 16 . dy . dx a. Use implicit differentiation to determine b. Find any point(s) on the curve where the tangent line to the curve is horizontal. Concepts: 6. Show that if x2 y 2 xy 42 , then dy y . dx x 7. A function y f ( x) is said to satisfy the Grand L. Liu Condition if it satisfies the formula f ( x) f ( x) 2 . Find all functions that satisfy the Grand L. Liu Condition. x