The derivative, f'(x), for a function f(x) is given by: $$ f'(x)=x^.5-3x^2 +1, x >-1$$ Find the function f(x).
If I am not wrong, the answer should be the integrated derivative: $$ f(x)=\frac{x^{1.5}}{1.5} - x^3 + x + c$$ Can someone confirm or correct me on this? I do not have access to the answer and the marker has marked this wrong. This is part (a) of the question.
To check consider
$$f(x)=\frac{x^{1.5}}{1.5} - x^3 + x + c$$
and compute
$$f'(x)=x^{.5} - 3x^2 + 1$$
that's always the best and maybe unique method to check.