## Jul 11, 2009

### 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

2. The two types of errors that are related to differentials are:
a) Human, Absolute.
b) Absolute, Relative.
c) Relative, Controllable.
d) Controllable, Natural.

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.

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.

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.

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.

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) &gt; 0
c) g ''(p) &lt; 0
d) There's no way to tell without first knowing what the specific function is.

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

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.