What is the extreme f(x)=x+4x^{-1} ?

The extreme f(x)=x+4x^{-1} is Maximum(-2,-4),Minimum(2,4)

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

extreme points

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

Maximum (- 2, - 4), Minimum (2, 4)

Solution steps

f^{'} (x) = 1 - \frac{4}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

x + 4 x^{- 1} : - 4

Maximum (- 2, - 4)

Plug

x = 2

into

x + 4 x^{- 1} : 4

Minimum (2, 4)

Maximum (- 2, - 4), Minimum (2, 4)

y = I n 9 - 2 x^{2}

f (x) = 2 x^{3} - 33 x^{2} + 144 x

f (x, y) = \frac{( x + y ) ^{2}}{2} - 2 ln (x y)

f (x, y) = ∣ x y ∣

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

What is the extreme f(x)=x+4x^{-1} ?
The extreme f(x)=x+4x^{-1} is Maximum(-2,-4),Minimum(2,4)