MCV4U1 - UNIT 2 - DERIVATIVES TEST ROUND ALL ANSWERS TO THE NEAREST TENTH, UNLESS OTHERWISE STATED. 1) Differentiate each of the following functions. Final answers should not contain negative or fraction exponents and should be simplified/factored as much as possible. 4x - 9x- + 6.x +5 3 a) f (x) =- (K - 3 marks) b) f (x) = (K - 3 marks) 2 (4x2 +2x- 7)c) f(x) = (6x2 -5)(2x -1)4 (K-3 marks) d) f(x) = 2+7x (5x2 -3) (K - 3 marks)4x + 5 e) f(x) = (A - 3 marks) x +1 f) f (x) = ] (A - 3 marks) 2 - 3 3x - 42) Find the derivative of f(x) = -7x3+5x -8 using first principles. (A - 3 marks)3) The owners of a restaurant are interested analyzing the productivity of their staff. The function NU} = 150 6131] ~.i'115+3r1 staff after {hours during an 8hour workday {D S I E 8) . Determine the rate, to the nearest models the total number ofeustorners, N, served by the tenth, at which the customers are being served at 4 hours. {A 3 marks) 4) Determine the equation of the tangent to f(x) = -x + 3x +1 that is perpendicular to the line J=-x+2. (I -6 marks)5) Find numbers a, b, and c such that the graph of y = ax + bx + c has x-intercepts of 0 and 8, and a tangent with a slope of 16 at x = 2. (1 -6 marks)6) Fill in the boxes below with integers to create the equation of another function that has the same tangent slopes as y = 48.x} + 424:2 Tx+ 5 at all xvalues. (C 2' marks} 7) Prove the Product Rule of differentiation. That is, prove that if p(x) = f(x)g(x), where f(x) and g(x) are differentiable, then p'(x) = f'(x)g(x)+g'(x)f(x). (C-4 marks)