Calculus I
Quiz # 6
October 16, 2002
Name____________________
R.  Hammack
Score ______


(1) Find the following derivatives.

(a)   [Graphics:Images/quiz6sol_gr_1.gif]         [Graphics:Images/quiz6sol_gr_2.gif][Graphics:Images/quiz6sol_gr_3.gif]


(b)   [Graphics:Images/quiz6sol_gr_4.gif]                               [Graphics:Images/quiz6sol_gr_5.gif]   [Graphics:Images/quiz6sol_gr_6.gif]



(c)   [Graphics:Images/quiz6sol_gr_7.gif][Graphics:Images/quiz6sol_gr_8.gif][Graphics:Images/quiz6sol_gr_9.gif]




(3) Suppose  [Graphics:Images/quiz6sol_gr_10.gif]  and  [Graphics:Images/quiz6sol_gr_11.gif]  Find all the values of x for which the slope of the tangent to [Graphics:Images/quiz6sol_gr_12.gif] at [Graphics:Images/quiz6sol_gr_13.gif] equals the slope of the tangent to  [Graphics:Images/quiz6sol_gr_14.gif] at [Graphics:Images/quiz6sol_gr_15.gif].

We are looking for all x that satisfy
f '(x) = g '(x)

[Graphics:Images/quiz6sol_gr_16.gif]

[Graphics:Images/quiz6sol_gr_17.gif]

[Graphics:Images/quiz6sol_gr_18.gif]

[Graphics:Images/quiz6sol_gr_19.gif]

[Graphics:Images/quiz6sol_gr_20.gif]

[Graphics:Images/quiz6sol_gr_21.gif] (difference of two squares)

[Graphics:Images/quiz6sol_gr_22.gif] (difference of two squares again)
  
x = 2 or x = -2

Thus, x equals plus or minus 2 is the answer to the question.