The discussion focuses on plotting the function f[r][x] = 1 + r*x + x^2 in Mathematica, specifically addressing how to visualize its derivatives. Users aim to differentiate the plot lines based on the sign of the derivative, using solid lines for negative derivatives and dashed lines for positive derivatives. The solution involves defining the critical points cps[r_] and using the Manipulate function to dynamically adjust the plot. The final implementation includes plotting the derived functions y[r_] and t[r_] with specific styles to indicate their derivative characteristics.
PREREQUISITESMathematica users, mathematicians, educators, and students interested in visualizing mathematical functions and their derivatives effectively.
f[r_][x_] := 1 + r*x + x^2;
A = Table[
cps[r_] = x /. Quiet[Solve[f[r][x] == 0, x], Solve::ratnz], {r, -5,
5, 0.01}];dwsmith said:Code:f[r_][x_] := 1 + r*x + x^2; cps[r_] = x /. Quiet[Solve[f[r][x] == 0, x], Solve::ratnz]
I want to then tell mathematica to check the derivative of f with each value from the table, plot the values, but make the lines where there derivative in less than 0 solid and dashed for greater than 0.
Any ideas on how to finish this?
f[r_][x_] := 1 + r*x + x^2;
cps[r_] = x /. Quiet[Solve[f[r][x] == 0, x], Solve::ratnz];
g[r_] = x /. Quiet[Solve[f[r][x] == 0, x], Solve::ratnz]
Plot[g[r], {r, -5, 5}, PlotStyle -> {Red, Thick}]
{1/2 (-r - Sqrt[-4 + r^2]), 1/2 (-r + Sqrt[-4 + r^2])}
Manipulate[Plot[f[r][x], {x, -4, 4}], {r, -10, 10}]
y[r_] = 1/2 (-r - Sqrt[-4 + r^2]);
t[r_] = 1/2 (-r + Sqrt[-4 + r^2]);
Plot[{y[r], t[r]}, {r, -5, 5},
PlotStyle -> {{Dashing[{Medium}], Red}, {Thick, Red}}]