BC 1
Quiz #7
Show all appropriate work clearly for full credit.
1.
Name:_________________
TI-30 CALCULATOR ALLOWED
For each function below, find its first derivative. Do not simplify the result.
a.
F  x   cosh(ln( x))  cos 1 (e x )
b. g  x  
tan 1 ( x3  3)
sec2 x
t
2.
Use the figure below to calculate the derivatives in a-c.
a.
g (2) if g ( x)  f  x 2 
b. k (2) if k ( x)  f 1 ( x)
c. h(4) if h( x)   f ( x) 
1
BC 1
3.
Quiz #7
Name:_________________
Consider the curve 4 x3  4 xy  y 2  4  0 .
dy
a) Determine
dx
b) Find the slope of the tangent line at all points on the graph with x  1 .
t
4. Suppose that z  x3  y 2 , where both x and y are changing with time. At a certain instant when x = 1
and y = 2, x is decreasing at a rate of 2 units/sec and y is increasing at a rate of 3 units/sec. How fast is z
changing at this instant? Is z increasing or decreasing?
BC 1
5.
Quiz #7
Name:_________________
Princess Yager (who is stationary) flies a kite at a constant height 120 feet above her hands. If
the wind carries the kite horizontally at the rate of 30 ft/min,
a. at what rate is the string being pulled out when there is 150 feet of string out?
b. at what rate is the angle of elevation of the kite changing when there is 150 feett of string out?
BC 1
6.
Quiz #7
Name:_________________
If V  10 h and h is a function of t with graph shown below, use this graph to estimate the value of
dV
when t = 2.
dt
h(t)
h(t)
300
200
100
t
t
0
-1
0
1
2
3
4
5
6
7