What is the extreme x+(31)/x ?

The extreme x+(31)/x is Maximum(-sqrt(31),-2sqrt(31)),Minimum(sqrt(31),2sqrt(31))

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extreme x+(31)/x

extreme points

x + \frac{31}{x}

Maximum (- 31, - 231), Minimum (31, 231)

Solution steps

f^{'} (x) = 1 - \frac{31}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 31,

Decreasing

: - 31 < x < 0,

Decreasing

: 0 < x < 31,

Increasing

: 31 < x < \infty

Plug

x = - 31

into

x + \frac{31}{x} : - 231

Maximum (- 31, - 231)

Plug

x = 31

into

x + \frac{31}{x} : 231

Minimum (31, 231)

Maximum (- 31, - 231), Minimum (31, 231)

f (x) = x^{4} + 4 x + 1

\frac{x ^{2} - 12}{x + 4}

f (x) = x^{4} - 8 x^{3} + 16 x^{2}

f (x) = 16 + 4 x - x^{2}, 0 \leq x \leq 5

f (x) = \frac{x ^{3}}{3} - x^{2} - 3 x - 1

What is the extreme x+(31)/x ?
The extreme x+(31)/x is Maximum(-sqrt(31),-2sqrt(31)),Minimum(sqrt(31),2sqrt(31))