Question

Find the maximum value of the function f(x) = x + x2

Answer 1

The derivative of $f(x) = x + x^2$ is $f'(x) = 1 + 2 x$. Equation $f'(x) = 0$ has solution $x = -\frac{1}{2}$, and the signs of the derivative change from negative to positive in the intervals $(-\infty, -\frac{1}{2})$ , $(-\frac{1}{2}, \infty)$ , hence $x = -1/2$ is a local minimum. The function is not bounded from above, hence its maximum value is $+\infty$.