What is the extreme f(x)=-7sec(x),-pi/3 <= x<= pi/3 ?

The extreme f(x)=-7sec(x),-pi/3 <= x<= pi/3 is Minimum(-pi/3 ,-14),Maximum(0,-7),Minimum(pi/3 ,-14)

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extreme f(x)=-7sec(x),-pi/3 <= x<= pi/3

extreme points

f (x) = - 7 sec (x), - \frac{π}{3} \leq x \leq \frac{π}{3}

Minimum (- \frac{π}{3}, - 14), Maximum (0, - 7), Minimum (\frac{π}{3}, - 14)

Solution steps

Find the critical points:

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

Domain of

- 7 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

- 7 sec (x) \Rightarrow y = - 14

Minimum (- \frac{π}{3}, - 14)

Plug the extreme point

x = 0

into

- 7 sec (x) \Rightarrow y = - 7

Maximum (0, - 7)

Plug the extreme point

x = \frac{π}{3}

into

- 7 sec (x) \Rightarrow y = - 14

Minimum (\frac{π}{3}, - 14)

Minimum (- \frac{π}{3}, - 14), Maximum (0, - 7), Minimum (\frac{π}{3}, - 14)

f (x, y) = \frac{x y ( 9 - x - 2 y )}{3}

x^{3} + 3 x y^{2} - 3 y^{2} - 3 x^{2} + 11

0.001 x^{2} + 3.4 x - 90

f (x) = 12 x - 12 y - 2 x^{2} - 3 y^{2} - 25

f (x) = 3 x^{3} + 9 x^{2} - 72 x

What is the extreme f(x)=-7sec(x),-pi/3 <= x<= pi/3 ?
The extreme f(x)=-7sec(x),-pi/3 <= x<= pi/3 is Minimum(-pi/3 ,-14),Maximum(0,-7),Minimum(pi/3 ,-14)