# What are the extrema of f(x) = 1 - sqrt(x)?

Dec 8, 2016

Max f = 1. There is no minimum.

#### Explanation:

$y = f \left(x\right) = 1 - \sqrt{x}$. Graph is inserted.

This represents a semi parabola, in the quadrants ${Q}_{1} \mathmr{and} {Q}_{4}$,

wherein x >=0.

Max y is at the end (0, 1). Of course, there is no minimum.

Note that, as $x \to \infty , y \to - \infty$.

The parent equation is ${\left(y - 1\right)}^{2} = x$ that can be separated into

$y = 1 \pm \sqrt{x}$.

graph{y+sqrtx-1=0 [-2.5, 2.5, -1.25, 1.25]}