What is the extreme f(x)=x^2+(200)/x ,(0,infinity) ?

The extreme f(x)=x^2+(200)/x ,(0,infinity) is Minimum(\sqrt[3]{100},100^{2/3}+(200)/(\sqrt[3]{100)})

Popular >

extreme f(x)=x^2+(200)/x ,(0,infinity)

extreme points

f (x) = x^{2} + \frac{200}{x}, (0, \infty)

Minimum (3100, 10 0^{\frac{2}{3}} + \frac{200}{3 100})

Solution steps

Find the critical points:

x = 3100

Domain of

x^{2} + \frac{200}{x}, (0, \infty) : x > 0

Find intervals:

Decreasing

: 0 < x < 3100,

Increasing

: 3100 < x < \infty

Plug the extreme point

x = 3100

into

x^{2} + \frac{200}{x} \Rightarrow y = 10 0^{\frac{2}{3}} + \frac{200}{3 100}

Minimum (3100, 10 0^{\frac{2}{3}} + \frac{200}{3 100})

f (x, y) = 9 - 2 \cdot x + 4 \cdot y - x^{2} - 4 \cdot y^{2}

f (x) = 5 x - 8 sin (x), 0 \leq x \leq π

f (x) = x (440 - 2 x)

x ln (4 x)

f (x) = 2 x^{2} + 7 x

What is the extreme f(x)=x^2+(200)/x ,(0,infinity) ?
The extreme f(x)=x^2+(200)/x ,(0,infinity) is Minimum(\sqrt[3]{100},100^{2/3}+(200)/(\sqrt[3]{100)})