MCV4U V.2
UNIT 5 TEST: DERIVATIVES OF EXPONENTIAL, LOG, AND TRIG FUNCTIONS
Name:
COMMUNICATION
KNOWLEDGE
/4
Date:
COMMUNCATION ‐ TEST
Enough steps shown to clearly demonstrate thinking
Solutions that are neat and easy to follow
Proper use of mathematical symbols and notation
Equal signs (aligned, one per line)
Side calculations clearly labeled if used
Units used as required
Variables and functions defined as required
COMMUNCATION ‐ UPLOAD
All work submitted as one PDF file (‐1 mark)
PDF file follows proper naming convention
LastName_FirstName_Chapter#_Test/Quiz
PDF files must be in portrait mode
APPLICATION
/10
THINKING
/9
/9
(2 MARKS)
Concluding statements used as required
Fractions, not decimals, unless otherwise stated
Radicals, not decimals, unless otherwise stated
Fractions reduced to lowest terms
Denominators rationalized
Labels, arrows, smooth lines, and ruler used as required
Labelled axis and titled graph
(2 MARKS)
PDF file must be submitted in the appropriate assignment / quiz location.
(‐2 marks)
PDF must contain the full page
PDF is in order (‐1 mark)
PDF must be clear and readable (‐2 marks)
UNSUPPORTED WORK WILL RECEIVE A MARK OF ZERO FOR THAT QUESTION.
KNOWLEDGE
1. Differentiate the following functions and find the slope of the tangent at the indicated point.
1
5
a)
f  x   sin  x  ln 5 x 
at x 
b)
y  ln x 
at x  e
c)
y
x ln  x 
cos x
at x  1
4
cos x
3
2. Let f  x  
3
log 3x
a
2

 2 . For what value of a is f ' 1  3 ? Make sure you convert the log function in ln.
APPLICATION
3. Find constants A and B such that the function y  A sin x  B cos x satisfies the differential equation
y ' ' y '2 y  sin x .
3
x
4. Find the maximum value and the minimum value of the function f  x   x 2e 2 , on the interval  1  x  6 .
3
cos x
 
 
 
. Find h'   .
  4 and f '    2 , and let h x  
f x 
3
3
3
5. Suppose f 
3
THINKING/INQUIRY
6. For what values of x does the graph of f  x   x  2 sin  x  have a horizontal tangent ?
3
7. Find the 35th derivative of the function g  x   x sin x  .
3
8. Let g  x   ecx  f  x  , where f 0   3 , f ' 0   5 and f ' ' 0   2 . Find g ' ' 0  , in terms of c .
3