4. Which of the following statements is correct? a. The derivative of a product is the product of the derivatives. b. The derivative of a quotient is the quotient of the derivatives. c. The derivative of a constant k is k. d. The derivative of a constant times a function is the same as the constant times the derivative of the function. e. The derivative of a power is the power of the derivative. 5. What is the derivative of the function f(x) = x + 2x _ _ + 5? X a. f '(x) = x +2x -1 b. f ( x ) = 3x + 4x -_ + 5 * 2 c. f '(x) = 3x + 4x- * 2 d. f '( x) = 3x + 4x + 6. What is the derivative of f(x) = cot x? (Hint: cot x = Cos x sin x a. f '(x) = cos x . sin x b. f ' (x) = sec x c. f '(x) = - csc x d. f '(x) = tan x e. f '(x) = cot x 7. In using the chain rule to calculate the derivative of f(x) = sin(4x + 1), you would let u stand for: a. u = sin x b. u = 4x + 1 C. U = 4x d. u= x 8. In using the chain rule to calculate the derivative of f(x) = (x + 2x + 1) , would equal du U a. True b. False Unit 2 Evaluation 178 MTHH 0719. Given the function f(x) = (x + 2) , calculate f "(-1). a. 2.000 b. 6.000 c. 3.000 d. -1.000 10. Which of the following functions are differentiable for all real numbers x? a. f(x) = sin x b. f(x) = tan x c. f(x) = 1 x| 11. If a function is differentiable at a point then it must also be continuous at that point. a. True b. False 12. If a function is continuous at a point then it must be differentiable at that point. a. True b. False 13. The equation of a circle centered at (0, 0) with a radius of 2 is x + y = 2". What is the slope of the tangent to the circle at the point (1, v/3 )? a. -1 b. - V3 3 C. - V2 2 d. - V3 e. none of these 14. What is the slope of the tangent line to x cos y - sin y = 0 at the point (0, 7 )? a. 0 -2 1 b. 272 C. -1 d. undefined Unit 2 Evaluation 179 MTHH 07115. The equation vy - cos x - 1 = 0 crosses the y-axis at one location. What is the slope of the tangent to the graph as it is crossing the y-axis? a. -1 b. 0 c. V2 d. 2 e. none of these 16. Find y ' if 2x - 3y = 4xy. a. 6x2 - 4y 4x +9y2 6 x2 b. 4x +9y2 6x2 - 92 - 4y 4 x d. 4x +9y2 6x2 - 4y 17. Find y 'if 8 xy + 6x = 3y. a. 4y + 6\\xy +4x 3 xy b . 3 xy - 4y 4 x 4x - 3 xy C. 6 xy + 4y 4y + 6 xy 3 xy - 4x WIN 18. Where is f(x) = (x - 2)3 differentiable? a. (-00, 00) b. (2, 00) C. (-00, 2) U (2, 00 ) d. (-00, 0) U (0, 00) Unit 2 Evaluation 180 MTHH 071Name ID. Number Unit 2 Evaluation 0 Evaluation 02 AP Calculus AB 1 (MTHH 071 057) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your course materials. You will need to understand, analyze, and apply the information you have learned in order to answer the questions correctly. To Submit the evaluation by mail. follow the directions on your Enrollment Information Sheet. To take the evaluation online. access the online version of your course; use the navigation panel to access the prep page for this evaluation and follow the directions provided. Note: A graphing calculator may be used on unit evaluations. You may also use scratch paper to work out the solutions. J Multiple-Choice Select the response that best completes the statement or answers the question. 'I. The slope of the tangent line to a function x) at a point where x = a is measured by which of the following? a. Iim f(x+h)f(x) xph h f(x + h) x) b. Iim h>0 m = f(x+h) f(x) (x+h)x d. f'(h) f(x + h) x} 2. If x) = x2, then Iim would be worth hpO a. 2 b. x2 + 2m + n2 C. X d. none of these 3. If x) = 3x + 5, then the value off 17:) is a. 3.500 b. 5.000 c. 3.000 d. 5.300 Unit 2 Evaluation 177 MTHH 071