What is the extreme f(x)=3-x-(25)/x ,x>0 ?

The extreme f(x)=3-x-(25)/x ,x>0 is Maximum(5,-7)

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extreme f(x)=3-x-(25)/x ,x>0

extreme points

f (x) = 3 - x - \frac{25}{x}, x > 0

Maximum (5, - 7)

Solution steps

Find the critical points:

x = 5

Domain of

3 - x - \frac{25}{x}, x > 0 : x > 0

Find intervals:

Increasing

: 0 < x < 5,

Decreasing

: 5 < x < \infty

Plug the extreme point

x = 5

into

3 - x - \frac{25}{x} \Rightarrow y = - 7

Maximum (5, - 7)

y = \frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 2 x

f (x, y, z) = 8 x + 8 y + 4 z = 5

f (x) = x^{3} - 6 x^{2} + 9 x + 9

f (x, y) = 2 x + 4 y - 5

- 2 x^{2} + 4 x + 3

What is the extreme f(x)=3-x-(25)/x ,x>0 ?
The extreme f(x)=3-x-(25)/x ,x>0 is Maximum(5,-7)