What is the extreme f(x)=-1/(x^2),0.5<= x<= 4 ?

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

Popular >

extreme f(x)=-1/(x^2),0.5<= x<= 4

extreme points

f (x) = - \frac{1}{x ^{2}}, 0.5 \leq x \leq 4

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

Solution steps

Find the critical points:

x = 0.5, x = 4

Domain of

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

Minimum (0.5, - 4)

Plug the extreme point

x = 4

into

- \frac{1}{x ^{2}} \Rightarrow y = - \frac{1}{16}

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

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

f (x) = x^{2} - \frac{54}{x ^{2}}

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

f (x, y) = x^{2} - 2 x + y^{2} - 6 y + 30

f (x, y) = e^{y l n (x)}

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

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