Calculus I Test #3 May 4, 2004
Name__________________ R. Hammack Score ______
____________________________________________________________
(1) Sketch the graph of the function
.![[Graphics:HTMLFiles/T3S04C_5.gif]](HTMLFiles/T3S04C_5.gif)
(2) Find the inverse of the function
. ____________________________________________________________
Calculus I Test
#3 May
4, 2004
Name__________________ R. Hammack Score
______
____________________________________________________________
(1) Sketch the graph of the
function .
(2) Find the inverse of the function
.
(3) Does the function 
have
an inverse? Explain.
(4) Solve the equation 
. (It's
OK to have logarithms in your final answer.)
(5) Simplify the following expressions as much as possible.
(a) ![FormBox[RowBox[{RowBox[{(-32), ^, 0.2}], =}], TraditionalForm]](HTMLFiles/T3S04C_15.gif){kind=small}
(b) 
(c) 
(d) 
(6) Find the following derivatives.
(a) ![d/dx[ e^(x ln(x) )] =](HTMLFiles/T3S04C_23.gif){kind=small}
(b) ![d/dx[ ( ln ( tan^(-1)(x) ) )^3 ] =](HTMLFiles/T3S04C_25.gif){kind=small}
(c) ![d/dx[ log_10(x) ] =](HTMLFiles/T3S04C_27.gif){kind=small}
(d) ![d/dx[sin^(-1)(x^(1/2))] =](HTMLFiles/T3S04C_29.gif){kind=small}
(7) The graph of the
derivative of a function f(x)
is drawn. Answer the following questions about the
function f(x).
![[Graphics:HTMLFiles/T3S04C_31.gif]](HTMLFiles/T3S04C_31.gif)
(a) Find the interval(s) on which f(x)
increases.
(b) Find the critical points
of 
.
(c) Find the locations of
the relative extrema of 
,
and identify them as relative maxima or minima.
(d) Find the intervals on
which the graph of f(x) is concave
up/down.
(8) These problems are about
the function 
.
Answer the following questions about f(x).
(a) Find the critical points of 
.
(b) Find the intervals of
increase/decrease of f(x).
(c) Find the locations of
the relative extrema of 
,
and identify them as relative maxima or minima.
(d) Find the intervals on
which the graph is concave up/down.