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Applications of calculus

Written by Hassan Raza (Mathematics)

NET · Mathematics · 5 questions

Name: ____________________   Date: ____________

  1. A rectangle has a perimeter of 20. What is the largest area it can have?

    • A 24
    • B 30
    • C 20
    • D 25

  2. A particle has speed v = 3t². How far does it travel from t = 0 to t = 2?

    • A 6
    • B 8
    • C 4
    • D 12

  3. What is the area under y = sin x from x = 0 to x = pi/2?

    • A 1
    • B 2
    • C pi / 2
    • D 0

  4. What is the equation of the tangent to y = x² at the point (1, 1)?

    • A y = 2x - 1
    • B y = x + 1
    • C y = 2x + 1
    • D y = x

  5. A function is increasing on an interval when its derivative is:

    • A Negative
    • B Positive
    • C Zero
    • D Undefined

Answer key

1. D, 2. B, 3. A, 4. A, 5. B

  1. The area is largest for a square. Each side is 5, so the area is 25.

  2. Distance is the integral of 3t², which is t³. Between 0 and 2 it equals 8.

  3. The integral is -cos x evaluated between 0 and pi/2, which is 0 - (-1) = 1.

  4. The slope is 2x = 2 at x = 1. Then y - 1 = 2(x - 1) gives y = 2x - 1.

  5. A positive derivative means the function rises as x increases.