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}}]The purpose of this function is to allow users to plot the graph of a mathematical function, as well as its derivative, in order to visualize the relationship between the two. This can aid in understanding the behavior of the function and its rate of change.
To input a mathematical function, you will need to define the function using the appropriate syntax. For example, if you wanted to plot the function f(x) = x^2, you would type f[x_]:= x^2. This tells Mathematica to define the function f with the variable x and its corresponding expression.
Yes, you can plot multiple functions by defining each function separately and then using the Plot function to plot them all on the same graph. For example, if you wanted to plot f(x) = x^2 and g(x) = x^3, you would first define both functions and then use the command Plot[{f[x], g[x]}, {x, -5, 5}] to plot them.
In order to plot the derivative of a function, you will first need to define the function using the f[r_][x_] syntax and then use the command Plot[f'[x], {x, -5, 5}]. This will plot the derivative of the function f over the range of values specified.
Yes, there are several options available for customizing the appearance of the graph, such as changing the color, style, and thickness of the lines. You can also add a title, labels for the axes, and a legend to the graph. Additionally, you can change the range of values for the x and y axes to zoom in or out on specific parts of the graph.