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Applications of calculus
5 NET Mathematics questions with answers and explanations.
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A rectangle has a perimeter of 20. What is the largest area it can have?
- 1 20
- 2 24
- 3 25
- 4 30
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Correct answer: 25
The area is largest for a square. Each side is 5, so the area is 25.
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A particle has speed v = 3t^2. How far does it travel from t = 0 to t = 2?
- 1 6
- 2 8
- 3 12
- 4 4
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Correct answer: 8
Distance is the integral of 3t^2, which is t^3. Between 0 and 2 it equals 8.
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What is the area under y = sin x from x = 0 to x = pi/2?
- 1 0
- 2 1
- 3 2
- 4 pi / 2
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Correct answer: 1
The integral is -cos x evaluated between 0 and pi/2, which is 0 - (-1) = 1.
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What is the equation of the tangent to y = x^2 at the point (1, 1)?
- 1 y = 2x - 1
- 2 y = x
- 3 y = 2x + 1
- 4 y = x + 1
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Correct answer: y = 2x - 1
The slope is 2x = 2 at x = 1. Then y - 1 = 2(x - 1) gives y = 2x - 1.
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A function is increasing on an interval when its derivative is:
- 1 Negative
- 2 Zero
- 3 Positive
- 4 Undefined
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Correct answer: Positive
A positive derivative means the function rises as x increases.