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Calculus I                                            Test #3                             May 4, 2004

Name__________________           R.  Hammack                   Score ______
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(1)  Sketch the graph of the function f(x) = e^(x - 1) - 2.

[Graphics:HTMLFiles/T3S04C_5.gif]

(2) Find the inverse of the function f(x) = (x + 1)/(x - 1).



(3) Does the function  g(x) = 2cos(x) + x  have an inverse?  Explain.




(4) Solve the equation   4  5^(x + 1) = 3.  (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]

(b) e^(2ln(3) + ln(5)) =

(c)  tan^(-1)(-3^(1/2)) =

(d)  cos^(-1)(cos((5π)/3)) =



(6)  Find the following derivatives.

(a)   d/dx[ e^(x ln(x) )] =

(b)   d/dx[   (  ln ( tan^(-1)(x) )   )^3 ] =


(c)   d/dx[  log_10(x) ] =


(d)    d/dx[sin^(-1)(x^(1/2))] =


(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]
(a) Find the interval(s) on which f(x) increases.

(b)  Find the critical points of f(x).

(c)  Find the locations of the relative extrema of f(x), 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 f(x) = 3x^4 - 4x^3. Answer the following questions about  f(x).

(a) Find the critical points of f(x).



(b)  Find the intervals of increase/decrease of f(x).



(c)  Find the locations of the relative extrema of f(x), and identify them as relative maxima or minima.



(d)  Find the intervals on which the graph is concave up/down.