What is the extreme f(x)= 1/x ,-2<= x<= 3 ?

The extreme f(x)= 1/x ,-2<= x<= 3 is Maximum(-2,-1/2),Minimum(3, 1/3)

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extreme f(x)= 1/x ,-2<= x<= 3

extreme points

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

Maximum (- 2, - \frac{1}{2}), Minimum (3, \frac{1}{3})

Solution steps

Find the critical points:

x = - 2, x = 3

Domain of

\frac{1}{x}, - 2 \leq x \leq 3 : - 2 \leq x < 0 or 0 < x \leq 3

Find intervals:

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 3

Plug the extreme point

x = - 2

into

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

Maximum (- 2, - \frac{1}{2})

Plug the extreme point

x = 3

into

\frac{1}{x} \Rightarrow y = \frac{1}{3}

Minimum (3, \frac{1}{3})

Maximum (- 2, - \frac{1}{2}), Minimum (3, \frac{1}{3})

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

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

f (x) = x^{\frac{1}{5}} (x + 3)

x^{3} + 3 x^{2} + 1

f (x) = - 5 x^{4} + 5 x^{3} - 10

What is the extreme f(x)= 1/x ,-2<= x<= 3 ?
The extreme f(x)= 1/x ,-2<= x<= 3 is Maximum(-2,-1/2),Minimum(3, 1/3)