Differential and Integral Calculus - Multiple Choice questions - Part I

1. If f(x) = 3x², then F(x) =

   a) 6x

   b) x³

   c) x³ + C

   d) 6x + C

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c)

2. The two types of errors that are related to differentials are:

    a) Human, Absolute.

    b) Absolute, Relative.

    c) Relative, Controllable.

    d) Controllable, Natural.

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b)

3. Mathematically, what is a differential?

    a) A gear box on the back end of your car.

    b) A word used a lot on a popular medical television series.

    c) A method of directly relating how changes in an independent variable affect changes in a dependent variable.

    d) A method of directly relating how changes in a dependent variable affect changes in an independent variable.

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c)

4. The 2nd derivative of a function at point P is 0, and concavity is positive for values to the right of P. What must the concavity be to the left of P for P to be an inflection point?

   a) The concavity must also be positive.

   b) The concavity must be negative.

   c) The concavity must be neutral (0).

   d) The concavity must be imaginary.

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b)

5. At what value of q is the concavity of w(q) = -2, if w(q) = q⁴ - 16?

    a) At q = fourth root of 14.

    b)At q = 0.

    c) Never; w(q) is always concave down.

    d) Never; w(q) is always concave up.

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d)

6. What is needed to fully determine an anti-differentiated function?

     a) A lot of luck.

     b) A boundary condition.

     c) What its value is at (0, 0).

     d) Its real world application.

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b)

7. It has been determined that g(p) has a maximum at p = -47.6. What can be said of the function's concavity at that point?

   a) g ''(p) = 0

   b) g ''(p) > 0

   c) g ''(p) < 0

   d) There's no way to tell without first knowing what the specific function is.

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c)

8. What are the values of C₀ and C₁ in d(t) = C₁ + C₀t - 16t², if d(1) = 4 and v(2) = -65?

    a) C₀ = -1, C₁ = 21

    b) C₀ = 1, C₁ = -21

    c) C₀ = -1, C₁ = 19

    d) C₀ = 0, C₁ = 1

Show Answer
a)

9. G(d) was determined to be 3d + C; here, C is called:

     a) the constant of differentiation.

     b) the constant of anti-differentiation.

     c) the constant of integration.

     d) the constant of death and taxes.

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c)

10. Does f(c) = (c + 2)³ − 2 have an inflection point? If so, where is it located?

     a) Yes, at (-2, -2).

     b) Yes, at (2, -2).

     c) Yes, at (8, -2).

     d) No.

Show Answer
a)