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Derivatives and Integrals

1. Let's say that f ''(k) = 0 @(13, -2). What does this mean?
A) There is definitely an inflection point at that location.
B) There might be an inflection point at that location.
C) There definitely is not an inflection point at that location.
D) There's no way to tell without first knowing what the specific function is.

2.What is the converted substitution form of ∫12x2 (x3 + 1)5 dx?

A) 4∫u5 du
B) ∫u5 du
C) ¼ ∫u5 du
D) This cannot be solved by the substitution method.

4. ∫1/x dx =

A) Undefined because you cannot divide by zero.
B) loge(x)
C) ln(x)
D) ln(x) + C

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

A) At q = .
B) At q = 0.
C) Never; w(q) is always concave down.
D) Never; w(q) is always concave up.

6. 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.

7. If f(x) = 3x2, then F(x) =

A) 6x
B) x3
C) x3 + C
D) 6x + C

9. 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.

10. 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.

11. 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.

12. If is in radians, then _____.
A) cos(&#952;)
B) 0
C) 1
D) This is indeterminate.

13. 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.

14.

A) dy/dx
B) &#8747;f(x)dx
C) Undefined
D) Indeterminate

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