I am confuse about question 'b'.i can do question 'a'.can anybody clarify me please.the questions are: a)On the same axes sketch the curves given by $y=(x+1)^3$ and $y=3x(x-1)$.
b)Explain how your sketch shows that there is only one solution to the equations $x^3+6x+1=0$.
Generally to find number of solution I would do like this $(x+1)^3=3x(x-1)$ or $(x+1)^3-3x(x+1)=0$ but $x^3+6x+1=0$ is whole new equation.
$$(x+1)^3=x^3+3x^2+3x+1$$ $$3x(x-1)=3x^2-3x$$ $$(x+1)^3-3x(x-1)=x^3+6x+1$$ Your graphs should look like this:https://www.desmos.com/calculator/s9xq3jnkbi and you can see that the graphs only have one intersection, so there is only one solution.