Homework, pp. 136--, #17, 47, 51
MAT128, Fall, 2015
Andy Long

#17

y[x_]:=(x^2+4x+3)/Sqrt[x]
y'[x]
Simplify[y'[x]]
Expand[y'[x]]

#47

f[x_]:=3x^15-5x^3+3
f'[x]
Plot[{f[x],f'[x]},{x,-1.1,1.1}
,PlotRange->{-10,10}
,AxesLabel->Automatic
, PlotLabel->"#47, p. 137"
]

#51

Clear[l,f,m,x0,y0]
f[x_]:=2x/(x+1)
x0=1 
y0=f[x0]
m=f'[x0]
l[x_]:=m(x-x0)+y0
l[x]
Plot[{f[x],l[x]},{x,0,2}
,PlotRange->{0,2}
,AxesLabel->Automatic
, PlotLabel->"#51, p. 137"
]