What are the critical points of $f(x) = x^2 + 2/x$ ?

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Answer 1 · 2016-12-02T14:12:13

$(1, 3)$ is the only critical point.

The critical points will occur when the derivative equals $0$ or is undefined .

$f'(x) = 2x + (0 xx x - 1 xx 2)/(x)^2$

$f'(x) = 2x - 2/x^2$

The derivative will be undefined at $x = 0$ . However, the function is also undefined at $x = 0$ , so this is not a critical point.

$0 = 2x - 2/x^2$

$0 = (2x^3 - 2)/x^2$

$0 = 2x^3 - 2$

$2 = 2x^3$

$1= x^3$

$x = 1$

The corresponding y-coordinate is

$f(1) = 1^2 + 2/1 = 3$

Hence, the only critical point is at $(1, 3)$ .

Hopefully this helps!

What are the critical points of f(x) = x^2 + 2/xf(x) = x^2 + 2/x?