BC Calculus 1
Sample Quiz
Show all appropriate work clearly for full credit.
NO CALCULATORS
1.
Name:
For each function shown below, find its first derivative. DO NOT simplify.
 e( x  2 x ) 
f ( x)  ln 

 cosh( x) 
2
a.
f  x 
b. g  x   tan 1 ( x3  3)  sec2 x
g  x  
2.
3.
Find f ''  x  if f ( x)  sin  x 2 
Find values of p and q such that the line y  px  5 is tangent to the graph of
q
 x   x3   1 at the point where x = 1.
x
3a. Suppose h( x)   f ( g ( x))  . Given the information about , g and their derivatives provided in
the table, fill in the missing information.
2
x
1
2
4
f  x
3
–1
5
f  x
–1
8
6
g ( x)
4
2
1
g ( x)
1
4
3
h( x )

h( x )

3b. Given the information above, suppose that k ( x)  f ( g ( x)) where k is one-to-one and
d
 k 1 ( x )  at x = 5.
differentiable. Evaluate the
dx
ln( x)  1
. Determine the exact value of x for which this function has a stationary
x
point, then determine whether k has a local max, a local min, or neither at this point. Be sure
to justify.
Let k  x  
4.
5.
Consider the curve defined by the equation 3 y3  12 x2 y  16 x3  16 .
dy
.
dx
a.
Use implicit differentiation to determine
b.
Find any point(s) on the curve where the tangent line to the curve is horizontal.
Concepts:
6. Show that if x2 y 2  xy  42 , then
dy  y

.
dx
x
7. A function y  f ( x) is said to satisfy the Grand L. Liu Condition if it satisfies the formula
f ( x)
f ( x)  2 . Find all functions that satisfy the Grand L. Liu Condition.
x