Given f'(x) = x2 + 2x − 3, find the turning points and intervals of increase/decrease of f(x)?

Factor the quadratic equation:

This gives two $x$-coordinates for the turning points:

For $x = -3$:

The first turning point is $(-3, 9+C)$.

For $x = 1$:

The second turning point is $(1, -\frac{5}{3}+C)$.

The coordinates of the turning points are $\boxed{(-3, 9+C) \text{ and } (1, -\frac{5}{3}+C)}$.

We found the roots of $f'(x) = 0$ to be $x = -3$ and $x = 1$.
Since $f'(x) = x^2 + 2x - 3$ is a parabola opening upwards (the coefficient of $x^2$ is positive), $f'(x)$ is positive outside its roots and negative between its roots.

$f(x)$ is increasing when $f'(x) > 0$:

This occurs when $x < -3$ or $x > 1$.

$f(x