348.sagews

pretty_print_default(enable=true)
var('t')
eq1a(t) = -5.29*t^2 + 53.61*t - 134.8
eq1b(t) = -6.52*t^2 + 79.61*t - 240.4

xmin = find_root(derivative(eq1a)==0,0,10) ; xmin

\newcommand{\Bold}[1]{\mathbf{#1}}5.06710775047

xmax = find_root(derivative(eq1b)==0,0,10) ; xmax

\newcommand{\Bold}[1]{\mathbf{#1}}6.10506134969

p1 = plot([eq1a,eq1b], xmin, xmax)
show(p1, xmin, xmax, 0, 3)

intsc = find_root(eq1a == eq1b, 1, 10) ; intsc

\newcommand{\Bold}[1]{\mathbf{#1}}5.48458638515

p1a = plot(eq1a(t+xmin), 0, intsc - xmin) ; p1a

p1b = plot(eq1b(t+xmin), intsc - xmin, xmax - xmin) ; p1b

p1a + p1b

Va(t) = derivative(eq1a) ; Va

\newcommand{\Bold}[1]{\mathbf{#1}}t \ {\mapsto}\ -10.5800000000000 \, t + 53.6100000000000

Va(intsc)

\newcommand{\Bold}[1]{\mathbf{#1}}-4.41692395488534

Vb(t) = derivative(eq1b) ; Vb

\newcommand{\Bold}[1]{\mathbf{#1}}t \ {\mapsto}\ -13.0400000000000 \, t + 79.6100000000000

Vb(intsc)

\newcommand{\Bold}[1]{\mathbf{#1}}8.09099353764606