 
Summary: Math 1441 Fall 2006
Sections 1 and 2 P. Achar
Exam 3 Solutions
November 9, 2006
Total points: 100 Time limit: 80 minutes
No calculators, books, notes, or other aids are permitted. You must show your work and justify your
steps to receive full credit.
1. (4 points each) Short answer:
(a) Explain what is wrong with the following statement: "The antiderivative of the function f(x) = 2x
is F(x) = x2
."
Solution: There is no such thing as the antiderivative; it should say: "An antiderivative . . . "
Alternatively, the statement could be corrected by saying, "The general antiderivative of f(x) = 2x
is F(x) = x2
+ C."
(b) What method did we use in class to find the derivatives of inverse trigonometric functions (such
as arcsin x) after we already knew the derivatives of the ordinary trigonometric functions? (Hint:
It's the same technique we used to find d
dx ax
when we already knew d
