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

The extreme f(x)=-2sec(x),-pi/3 <= x<= pi/3 is Minimum(-pi/3 ,-4),Maximum(0,-2),Minimum(pi/3 ,-4)

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

extreme points

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

Minimum (- \frac{π}{3}, - 4), Maximum (0, - 2), Minimum (\frac{π}{3}, - 4)

Solution steps

Find the critical points:

x = - \frac{π}{3}, x = 0, x = \frac{π}{3}

Domain of

- 2 sec (x), - \frac{π}{3} \leq x \leq \frac{π}{3} : - \frac{π}{3} \leq x \leq \frac{π}{3}

Find intervals:

Increasing

: - \frac{π}{3} < x < 0,

Decreasing

: 0 < x < \frac{π}{3}

Plug the extreme point

x = - \frac{π}{3}

into

- 2 sec (x) \Rightarrow y = - 4

Minimum (- \frac{π}{3}, - 4)

Plug the extreme point

x = 0

into

- 2 sec (x) \Rightarrow y = - 2

Maximum (0, - 2)

Plug the extreme point

x = \frac{π}{3}

into

- 2 sec (x) \Rightarrow y = - 4

Minimum (\frac{π}{3}, - 4)

Minimum (- \frac{π}{3}, - 4), Maximum (0, - 2), Minimum (\frac{π}{3}, - 4)

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

f (x, y) = 4 x^{2} + 4 y^{2}

P (a, c) = a + 7 + c

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

P (x, y) = 2 x + 2 y - x^{2} + y^{2}

What is the extreme f(x)=-2sec(x),-pi/3 <= x<= pi/3 ?
The extreme f(x)=-2sec(x),-pi/3 <= x<= pi/3 is Minimum(-pi/3 ,-4),Maximum(0,-2),Minimum(pi/3 ,-4)