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\noindent
MATH 180\hfill FALL 1995
\centerline{ASSIGNMENT \#21}
 
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4.1, \#2.  The derivatives of the linear functions
$$r(t)=2t-4 \hbox{ and  } s(t)=3r(t)=6t-12$$
are the slopes of their graphs.
Thus $r'(t)=2$, $s'(t)=6$, and $s'(t)=3r'(t)$.
 
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4.2, \#2, 4, 5.
$$\vbox{
\halign{ $#$\qquad & $\displaystyle #$& \quad\qquad $\displaystyle
     #$\hfil & \quad\qquad $\displaystyle #$\hfil  \cr
    y  &  \phantom{-12}x^{-12} & \phantom{(3/4)}x^{3/4} &
          \phantom{-(3/4)}x^{-3/4} \cr
   \noalign{\vskip3pt}
   \noalign{\hrule}
   \noalign{\vskip3pt}
    y' &  -12x^{-13} & (3/4) x^{-1/4} & -(3/4)
x^{-7/4}\cr}}$$
 
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4.2, \#6, 11, 12
$$\vbox{
\halign{ $#$\qquad & $\displaystyle #$& \quad\qquad $\displaystyle
    #$\hfil & \quad\qquad $\displaystyle #$\hfil  \cr
    y &  \phantom{-4}x^{-4} & -\phantom{1}3x^4-4x^3-6x+2
       & \phantom{1}3t^5-5\sqrt t+7/t\cr
   \noalign{\vskip3pt}
   \noalign{\hrule}
   \noalign{\vskip3pt}
    y' & -4x^{-5} & -12x^3-12x^2-6 &
      15t^4-(5/2)t^{-1/2}-7t^{-2}\cr}}$$
 
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4.2, \#30.  If $f(t)=2t^3-4t^2+3t-1$, then
$$f'(t)=6t^2-8t+3,\qquad f''(t)=12t-8.$$
 
 
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