University:
Concordia University Texas
Course:
MTH 3101 | Problem Solving: Algebra, Geometry, and Trigonometry
Academic year:

2022
Views:

243

Pages:

8
Author:

Marianna B

Unit 5 Progress Check: MCQ Part B The second derivative of the function / is given by f^ prime prime (x) = x ^ 2 * cos((x ^ 2 + 2x)/6) . the interval (-4, 3) does the graph of f have a point of inflection? At what values of in A) 2.229 only B) 0 and 2.229 c) -2.357 and 0.987 D) 3.259, 0, and 1.603 2. The second derivative of the function f is given by f^ prime prime (x) = sin((x ^ 2)/u) - 2 cos z. The function / has many critical points, two of which are at true? x = 0 and x = 6.949 Which of the following statements is A has a local minimum at and at x = 0 6.949. B) has a local minimum at and a local maximum at x = 6.949 x = 0 c) has a local maximum at x = 0 and a local minimum at x = 6.949 D) has a local maximum at 0 and al z = 6.949. 3. Let/be the function given by f(x) = 2x ^ 3 + 3x ^ 2 + 1 What is the absolute maximum value of f on the closed interval [-3,1]? Unit 5 Progress Check: MCQ Part B A) 1 B) 2 C6 D) 26 4. Let/be the function defined by f(x) = sin x + cos x What is the absolute minimum value of fon the interval [0, 2x]? A)-2 B - sqrt(2) C-1 DO 5. Let 9 be the function defined by g(x) = (x ^ 2 - x + 1) * e ^ x What is the absolute maximum value of 9 on the interval [4,1]? Unit 5 Progress Check: MCQ Part B A) 1 2/c 21/(e ^ 4) 6. 1- - 5-4-3-2-1 1 2 3 4 5 6 7 8 Graph of t' The graph f' the derivative of the function f is shown above. On which of the following open intervals is the graph off concave down? AP Callingboard AP Calculus AR Scoring Guide Unit 5 Progress Check: MCQ Part B A) (-5,-3) and (1,6) B) (-3,1) and (6,8) C) (-1,4) D(4,8) 7. y 40- 30+ 20- 10+ + -3 -1 1 -10- 2 +x 3 -2 -20- -30- -40+ Graph of f Let f be the function defined by f(x)=102. The graph of f', the derivative off, is shown above. On which of the following intervals is the graph of f concave up? Unit 5 Progress Check: MCQ Part B x < - sqrt(3) and 0 < x < sqrt(3) - sqrt(3) < x < 0 and x > sqrt(3) x < - sqrt(6) x > sqrt(6) - sqrt(6) < x < sqrt(6) 8. The Second Derivative Test cannot be used to conclude that x = 2 the location of a relative minimum or relative maximum for which of the following functions? A f(x) = cos(x - 2) where f' * (x) = - sin(x - 2) f(x) = x * e ^ (- x/3) where f' * (x) = e ^ (- x/3) - 1/2 * x * e ^ (- x/3) f(x) = x ^ 2 - 4x - 2 where f' * (x) = 2x - 4 D f(x) = x ^ 3 - 6x ^ 2 + 12x + 1 where f' * (x) = 3x ^ 2 - 12x + 12