Plot inequalities

Teaching my son howto determine domain for inequalities and plot.

x^3 -5x^2 -9x +45 <= 0

so (x+3)(x-3)(x-5) <=0

so critical points are 3,-3 and 5.

Next plot graph using derivatives.
1st derivative is 3x^2 -10x -9 which is zero for x approx 4 or x approx -2/3.
2nd drivative is -ve for x=4 and +ve for x=2/3.
Plot and you will find 2 regions where graph is in 3rd and 4th quadrant (y is -ve or <0)
1st region where y<=0 is x between 3 and 5 and 2nd region where y<=0 is x< -3. and these are the two answers