Section 3.1 Examples
MAT128, Fall, 2015
Andy Long

#22, p. 205

f[x_]:=Cos[x]
Plot[{f[x],f'[x]},{x,-3Pi/2,3Pi/2}]

#31, p. 205

f[x_]:=2x^3-3x^2-36x
f'[x]
Solve[f'[x]==0,x]
Plot[{f[x],f'[x]},{x,-3,4}]

#45, p. 205

f[x_]:=12+4x-x^2
f'[x]
Solve[f'[x]==0,x]
Plot[{f[x],f'[x]},{x,0,5}]

#63, p. 205

V[T_]:=999.87-.06426T+.0085043T^2-.0000679T^3
V'[T]
Solve[V'[T]==0,T]

Plot[V[T],{T,0,30}]
(* where the volume is a minimum, the density will be a maximum (since rho=mass/volume)
*)

#67, p. 206

Clear[r,k,r0]
v[r_]:=k(r0-r)r^2
Simplify[v'[r]]
r0=1
k=1
Plot[{v[r]},{r,r0/2,r0}]
Plot[{v[r],v'[r]},{r,r0/2,r0},PlotRange->{-.4,.4}]