`g'(x) = 4x^2, g(-1) = 3` Find the particular solution that satisfies the differential equation.
You need to use direct integration to evaluate the general solution to the differential equation:
`int (4x^2)dx = 4x^3/3 + c`
You need to find the particular solution using the information provided by the problem, that g(-1) = 3, such that:
`g(-1) = (4/3)*(-1)^3 + c => 3 = -4/3 + c => c = 3 + 4/3 => c = 13/3`
Hence, evaluating the particular solution to the given differential equation yields `g(x) = 4x^3/3 + 13/3.`