# How do you find the maximum value of y=x^2+2x+3?

Sep 19, 2016

There is no maximum value.

#### Explanation:

1) The graph is an upward opening parabola; there is no maximum.

2) ${\lim}_{x \rightarrow \infty} \left({x}^{2} + 2 x + 3\right) = \infty$, so there is no maximum.

Using $y = f \left(x\right)$,

3) $f ' \left(x\right) = 2 x + 2 = 0$ at $x = - 1$. Therefore, $- 1$ is the only critical number and the first or second derivative test will show that $f \left(- 1\right)$ is a minimum, not a maximum.