CRL 5.1 MrG Direction of a curve

3616 days ago by calcpage123

f(x)=x^3/3-x^2+2 g(x)=diff(f(x),x) show(f(x)) show(g(x)) show(g(3)) angle=atan(g(3)) show((angle).n()) show((angle*180/pi).n()) y = g(3)*(x-3)+f(3) show(y) plot([f(x),y],xmin=-2,xmax=3,aspect_ratio=1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{3} \, x^{3} - x^{2} + 2
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} - 2 \, x
\newcommand{\Bold}[1]{\mathbf{#1}}3
\newcommand{\Bold}[1]{\mathbf{#1}}1.24904577239825
\newcommand{\Bold}[1]{\mathbf{#1}}71.5650511770780
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x - 7
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{3} \, x^{3} - x^{2} + 2
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} - 2 \, x
\newcommand{\Bold}[1]{\mathbf{#1}}3
\newcommand{\Bold}[1]{\mathbf{#1}}1.24904577239825
\newcommand{\Bold}[1]{\mathbf{#1}}71.5650511770780
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x - 7
solve(g(x)==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = 0, x = 2\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = 0, x = 2\right]
l=solve(g(x)==1,x) show(l) show(l[0]) show(l[1]) show(l[0].rhs().n()) show(l[1].rhs().n()) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\sqrt{2} + 1, x = \sqrt{2} + 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}x = -\sqrt{2} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x = \sqrt{2} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}-0.414213562373095
\newcommand{\Bold}[1]{\mathbf{#1}}2.41421356237309
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\sqrt{2} + 1, x = \sqrt{2} + 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}x = -\sqrt{2} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x = \sqrt{2} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}-0.414213562373095
\newcommand{\Bold}[1]{\mathbf{#1}}2.41421356237309
l=solve(g(x)==2/3,x) show(l) show(l[0]) show(l[1]) show(l[0].rhs().n()) show(l[1].rhs().n()) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\frac{1}{3} \, \sqrt{15} + 1, x = \frac{1}{3} \, \sqrt{15} + 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}x = -\frac{1}{3} \, \sqrt{15} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x = \frac{1}{3} \, \sqrt{15} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}-0.290994448735806
\newcommand{\Bold}[1]{\mathbf{#1}}2.29099444873581
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\frac{1}{3} \, \sqrt{15} + 1, x = \frac{1}{3} \, \sqrt{15} + 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}x = -\frac{1}{3} \, \sqrt{15} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x = \frac{1}{3} \, \sqrt{15} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}-0.290994448735806
\newcommand{\Bold}[1]{\mathbf{#1}}2.29099444873581