(a) '= . = . f A. (b) A'= f (c) A F 2. If is an area function for and is any antiderivative of then A f F f, (a) where is an arbitrary constant. F = A + C, C (b) = where is an arbitrary constant. f F + C, C (c) '= . f F 3. The value of (a) 0. (b) 1. (c) 2. 4. The value of (a) 0. (b) (c) x2. t2. The value of 5. (a) 0. (b) (c) x2. t2. 6. Consider the following three integrals: = = = 11 12 13 (a) = (b) = (c) = 11 12. 11 13. 12 13. 7. The function for > 0 is x (a) constant. (b) decreasing. (c) increasing. 8. The function (a) satisfies = 1. (b) has a local maximum at = . (c) satisfies = 0. g(0) x g(π) π 9. The value of is (a) ) - h'( y h'(1). (b) (c) - h(y). h(y) h(1). 10. is true of , if < ? a b (a) It is an area of a region so it is nonnegative. (b) It may be positive or negative because it is a net area of a region. (c) It is less than Quick Quiz 5.3 Answers 1b 2a 3c 4a 5b 6a 7c 8b 9c 10a Section 5.4 Quick Quiz 1. The function ( = + 3x + f x) x3 x-1
(a) f '= A. (b) A'= f . (c) A = F . 2. If A is an area function for f and F is any antiderivative of f, then (a) F = A + C, where C is an arbitrary constant. (b) f = F + C, where C is an arbitrary constant. (c) f '= F . 3. The value of (a) 0. (b) 1. (c) 2. 4. The value of (a) 0. (b) x2. (c) t2. 5. The value of (a) 0. (b) x2. (c) t2. 6. Consider the following three integrals: 11 = 12 = 13 = (a) 11 = 12. (b) 11 = 13. (c) 12 = 13. 7. The function for x > 0 is (a) constant. (b) decreasing. (c) increasing. 8. The function (a) satisfies g(0) = 1. (b) has a local maximum at x = π . (c) satisfies g(π) = 0. 9. The value of is (a) h'( y ) - h'(1). (b) h(y). (c) h(y) - h(1). 10. is true of , if a < b ? (a) It is an area of a region so it is nonnegative. (b) It may be positive or negative because it is a net area of a region. (c) It is less than Quick Quiz 5.3 Answers 1b 2a 3c 4a 5b 6a 7c 8b 9c 10a Section 5.4 Quick Quiz 1. The function f ( x) = x3 + 3x + x-1
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