QuestionIf $f(x)=\int_{0}^{x}\left(16-t^{2}\right) e^{t^{3}} d t$ for all $x$, then find the largest open interval on which $f$ is increasing. Answer (in interval notation): $\square$

Studdy Solution
Identify the largest open interval where $f'(x) > 0$.
From the inequality $-4 < x < 4$, the largest open interval where $f(x)$ is increasing is:
$$(-4, 4)$$
The largest open interval on which $f$ is increasing is $\boxed{(-4, 4)}$.