Page 333 - Calculus Demystified

320
7 2 Final Exam
3
34. Let g(x) = x + x − 10x + 2. Then the graph of f is
2
(a) increasing on (−∞, −10/3) and decreasing on (−10/3, ∞)
(b) increasing on (−∞, 1) and (10, ∞) and decreasing on (1, 10)
(c) increasing on (−∞, −10/3) and (1, ∞) and decreasing on
(−10/3, 1)
(d) increasing on (−10/3, ∞) and decreasing on (−∞, −10/3)
(e) increasing on (−∞, −10) and (1, ∞) and decreasing on
(−10, 1)
3
2
35. Find all local maxima and minima of the function h(x) =−(4/3)x +5x −
4x + 8.
(a) local minimum at x = 1/2, local maximum at x = 2
(b) local minimum at x = 1/2, local maximum at x = 1
(c) local minimum at x =−1, local maximum at x = 2
(d) local minimum at x = 1, local maximum at x = 3
(e) local minimum at x = 1/2, local maximum at x = 1/4
36. Find all local and global maxima and minima of the function h(x) = x +
2 sin x on the interval [0, 2π].
(a) local minimum at 4π/3, local maximum at 2π/3, global minimum
at 0, global maximum at 2π
(b) local minimum at 2π/3, local maximum at 4π/3, global minimum
at 0, global maximum at 2π
(c) local minimum at 2π, local maximum at 0, global minimum at 4π/3,
global maximum at 2π/3
(d) local minimum at 2π/3, local maximum at 2π, global minimum at
4π/3, global maximum at 0
(e) local minimum at 0, local maximum at 2π/3, global minimum at
4π/3, global maximum at 2π
3
37. Find all local and global maxima and minima of the function f(x) = x +
2
x − x + 1.
(a) local minimum at −1, local maximum at 1/3
(b) local minimum at 1, local maximum at −1/3
(c) local minimum at 1, local maximum at −1
(d) local minimum at 1/3, local maximum at −1
(e) local minimum at −1, local maximum at 1

38. A cylindrical tank is to be constructed to hold 100 cubic feet of liquid.
The sides of the tank will be constructed of material costing $1 per