What is the extreme f(x,y)=-4/(x^2),0.5<= x<= 4 ?

The extreme f(x,y)=-4/(x^2),0.5<= x<= 4 is Minimum(0.5,-16),Maximum(4,-1/4)

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extreme f(x,y)=-4/(x^2),0.5<= x<= 4

extreme points

f (x, y) = - \frac{4}{x ^{2}}, 0.5 \leq x \leq 4

Minimum (0.5, - 16), Maximum (4, - \frac{1}{4})

Solution steps

Find the critical points:

x = 0.5, x = 4

Domain of

- \frac{4}{x ^{2}}, 0.5 \leq x \leq 4 : 0.5 \leq x \leq 4

Find intervals:

Increasing

: 0.5 < x < 4

Plug the extreme point

x = 0.5

into

- \frac{4}{x ^{2}} \Rightarrow y = - 16

Minimum (0.5, - 16)

Plug the extreme point

x = 4

into

- \frac{4}{x ^{2}} \Rightarrow y = - \frac{1}{4}

Maximum (4, - \frac{1}{4})

Minimum (0.5, - 16), Maximum (4, - \frac{1}{4})

x e^{- 5 x}

f (x) = 4 x y + 50 y - 9 y^{2} - \frac{1}{10} x^{2} y - 130

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

f (x) = 4 x^{3} - 108 x^{2} + 729 x

f (x) = 4 x^{\frac{3}{4}} - x, 0 \leq x \leq 256

What is the extreme f(x,y)=-4/(x^2),0.5<= x<= 4 ?
The extreme f(x,y)=-4/(x^2),0.5<= x<= 4 is Minimum(0.5,-16),Maximum(4,-1/4)