Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![f(x) = -12x° + 75x - 80x³
40. f(x) = x² - 2 In x
41. f(x) = -2x4 + x2 + 10
42. f(x)
8x3
15x2
+ 8
4.
3.
43. f(x)
= xe²/2
44. f(x)
= tan
x2
+ 2
45-54. First Derivative Test
a. Locate the critical points of f.
b. Use the First Derivative Test to locate the local maximum and mini-
mum values.
C. Identify the absolute maximum and minimum values of the function
on the given interval (when they exist).
45. f(x) = x² + 3 on [-3, 2]
46. f(x) = -x² - x + 2 on [-4, 4]
47. f(x) = xV4 – x² on [-2, 2]
48. f(x) = 2x³ + 3x2 - 12x + 1 on [-2, 4]
49. f(x) = -x² + 9x on [-4, 3]
50. f(x) = 2x - 5x - 10x + 4 on [-2, 4]
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51. f(x) = x³/*(x – 5) on [-5, 5]
52. f(x) =
on [-4, 4]
- 1
Isool 2at
53. f(x) = Vx In x on (0, co)
54. f(x) = x- 2 tanx on [-V3, V3]
55-58. Absolute extreme values Verify that the following functions
satisfy the conditions of Theorem 4.9 on their domains. Then find tF
location and value of the absolute extrema guaranteed by the theor
56. f(x) = 4x + 1/Vx
55. f(x) = xe*
57. A(r) = 24/r + 2mr, r> 0
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58. f(x) = xV3 - x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9cddc856-562e-4ce0-8c66-1fac8082cbe1%2F40108fcd-eae7-486c-a094-6a2f96a35743%2F466os9_processed.jpeg&w=3840&q=75)
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