BC 1
Sample Quiz
Show all appropriate work clearly for full credit.
Name:_________________
NO CALCULATORS
Skills:
1.
For each function below, find its first derivative. Do not simplify the result.
a.

g  x   sinh(2 x)  sin 1 ( x 2 )

5
g(x) =
b.
k  x   tan 1  cosh x 
k ( x ) =
2.
Suppose f  2  4, f   2  6, f  4  8, f   4  1, f 8  2, and f  8  3. If f is invertible and
everywhere differentiable, then what is the value of derivative of f 1  x  at x = 4?
3.
4.
dk
1
If k ( x)  tan 1  x   tan 1   , determine
, simplifying completely.
dx
 x
Consider the curve defined by the equation 3 y  12 x y  16 x  16 .
dy
a.
Use implicit differentiation to determine
.
dx
b. Find any point(s) on the curve where the tangent line to the curve is horizontal.
3
c.
2
3
Find the equations of all the tangent lines to the curve at x = 1.
5. Use the graph below to estimate  f 1  (3) .
BC 1
Sample Quiz
Name:_________________
dy
if sin(3x  y)  y 2 cos x .
dx
6.
Find
7.
The length of a rectangle is increasing at the rate of 4 cm/sec and the width is decreasing at the
rate of 2 cm/sec. What is the rate of change of the area of the rectangle when the area is 15 and
the width is 3 cm? Include units in your final answer.
8.
At a certain moment, one bicyclist is 4 miles east of an intersection, traveling toward the
intersection at the rate of 9 miles/hour. At the same time, a second bicyclist is 3 miles south of
the intersection traveling away from the intersection at the rate of 10 miles/hour. Is the distance
between the bicyclists increasing or decreasing at that moment? At what rate?
9.
If h(t ) 
2
dV
and V is a function of h with graph shown below, estimate the value of
when
dt
t
h  1 . (Show work and/or explain reasoning).