Question

PLEASE USE MATLAB COMMANDS THANK YOU

Use Matlab to graph the functions f(x) = 3xsin(3x) and g(x)= 12 - 2x² so that you can read off the point(s) of intersection (if any), accurate up to two decimal places. 1) Write down the Matlab command(s) you used to create the x-vector. 2) Write down the Matlab command(s) you used to produce the vectors containing the f- and g-function values. 3) Write down the Matlab command(s) you used to plot the graphs. 4) Write down the intersection point(s), accurate to two decimal places in each coordinate).

Answer 1

MATLAB CODE

%defining the function f(x) and g(x)

%. dot command allows for element wise multiplication this is what allows us to use f1=f(x) and g1=g(x)
f=@(x) 3.*x.*sin(3.*x);
g=@(x) 12-2.*(x.^2);

%command to create x vector from -10 to 10 with 0.01 spacing
x=-10:0.01:10;

%producing the vector of f(x) and g(x) and storing in f1 and g1
f1=f(x);
g1=g(x);

%Plotting x Vs f(x) and xVs g(x)
plot(x,f1);
%hold on is used to plot 2 many plots in one figure
hold on
plot(x,g1);

xlabel("x")
ylabel("f(x),g(x)")
legend("f(x)","g(x)")

OUTPUT

The intersection points can be seen on the graph

x1,y1=(-2.21,2.23) x2,y2=(2.21,2.23)

X -2.21 Y 2.2318 X 2.21 Y 2.2318 (x)6*(x)} -150 -200 -10 -8 6 4 2 0 2 4 6 8 10