write down an equation g(x) such that its root g(x) = 0 occurs when x = 7^(1/3). Differentiate it to obtain g’(x). I dont understand how to do this....
it also says while e < 10^(–5)
Any thoughts?
You are misreading the question. It certainly does NOT say "the equation g(x)" because "g(x)" is not an equation. Also you cannot mean that g(x)= 0 is a solution of an equation because the solution of an equation is a number, not another equation.
You mean that $\displaystyle x= 7^{1/3}$ is a root of the equation g(x)= 0. Take the third power of each side: $\displaystyle x^3= 7$ and then $\displaystyle g(x)= x^3- 7= 0$. Can you differentiate that?