136.169, Assignment No. 3
November 22 , 2002
The assignment is due Friday, November 29, 2002 in class. Late assignments receive a mark zero.
- Assume
that the function f(x) satisfies f’(x)=
, and that f is one-to-one.
If y = 
(x) , show that dy/dx=y . [5]
- Find
y’ =
, given that:
a) y= f’(x)
, where f(x)= 
, [4]
b) 
. [4]
c) 
. [3]
3. If f(x) =
, show that f’(x)>0 on (0,e) and f’(x) < 0
on (e,
) . What is the
value of f at x=e? Use the above to show that 
. [7]
4.a) Show that for x > 0 we
have that 
. [5]
b) Let f(x) = 
. What is the domain of f? Where is f differentiable?
Show that the derivative of f ( where ever it exists) is either 1 or –1.
Where is f continuous? Draw the graph of f. [7]
5.You are riding on a Ferris wheel of diameter 20m. The wheel is rotating at 1 revolution per minute. How fast are you rising or falling when you are 6m horizontally away from the vertical line passing through the center of the wheel? [7]
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Total [ 42/40]