What is the extreme f(x)=100+1/2 x+(1800)/x ?

The extreme f(x)=100+1/2 x+(1800)/x is Maximum(-60,40),Minimum(60,160)

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extreme f(x)=100+1/2 x+(1800)/x

extreme points

f (x) = 100 + \frac{1}{2} x + \frac{1800}{x}

Maximum (- 60, 40), Minimum (60, 160)

Solution steps

f^{'} (x) = - \frac{1800}{x ^{2}} + \frac{1}{2}

Find intervals:

Increasing

: - \infty < x < - 60,

Decreasing

: - 60 < x < 0,

Decreasing

: 0 < x < 60,

Increasing

: 60 < x < \infty

Plug

x = - 60

into

100 + \frac{1}{2} x + \frac{1800}{x} : 40

Maximum (- 60, 40)

Plug

x = 60

into

100 + \frac{1}{2} x + \frac{1800}{x} : 160

Minimum (60, 160)

Maximum (- 60, 40), Minimum (60, 160)

f (x) = \frac{x}{x ^{2} - 9}

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 1, - 2 \leq x \leq 3

f (x, y) = 25 - x^{2} - y^{2}

f (x, y) = x^{2} + y^{2} + x^{2} y + 4

f (x, y) = x^{2} + x y + y^{2} + 3 x - 3 y + 4

What is the extreme f(x)=100+1/2 x+(1800)/x ?
The extreme f(x)=100+1/2 x+(1800)/x is Maximum(-60,40),Minimum(60,160)