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.
a.
f ( x)  e ( x
2
2 x )
 cos( x)
f  x 
b.
g(x) 
sin 5 (3x 2  4 x)
sinh( x 2 )
g  x  
2.
Suppose h( x)  f ( g ( x)) . Given the information about , g and their derivatives provided in
the table, fill in the missing information.
x
1
2
4
f  x
5
–2
5
f  x
–1
8
6
g ( x)
2
4
1
g ( x)
9
4
3
h( x )
h( x )


3.
Consider the function f whose graph is given below:
Let h( x) 
f ( x2 )
.
x
a. Estimate the value of h
 3  . Show all the work leading to your answer.
b. Is h increasing or decreasing at x = 1? Justify your answer.
4. Suppose h( x)  f ( g ( x)) . Find a formula for h( x ) involving , g and their derivatives.
5.
An open topped box is to be made by cutting out squares with sides of x inches from each corner a
rectangular (10 inch x 16 inch) sheet of cardboard, then turning the sides up. Find the value of x
which will maximize the volume of the box.
10
16
x
x