What is the extreme f(x)=7sin^2(x)-14cos(x) ?

The extreme f(x)=7sin^2(x)-14cos(x) is Minimum(2pin,-14),Maximum(pi+2pin,14)

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extreme f(x)=7sin^2(x)-14cos(x)

extreme points

f (x) = 7 sin^{2} (x) - 14 cos (x)

Minimum (2 πn, - 14), Maximum (π + 2 πn, 14)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

7 sin^{2} (x) - 14 cos (x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn < x < π + 2 πn,

Decreasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

7 sin^{2} (x) - 14 cos (x) \Rightarrow y = - 14

Minimum (2 πn, - 14)

Plug the extreme point

x = π + 2 πn

into

7 sin^{2} (x) - 14 cos (x) \Rightarrow y = 14

Maximum (π + 2 πn, 14)

Minimum (2 πn, - 14), Maximum (π + 2 πn, 14)

f (x) = - 3 x^{2} - 30 x - 21

y = z - x

S (r, α) = r α

f (x, y) = 5004 + x^{2} + y^{2}

f (x) = 2 x^{3} - 6 x^{2} - 210 x + 1, - 6 \leq x \leq 8

What is the extreme f(x)=7sin^2(x)-14cos(x) ?
The extreme f(x)=7sin^2(x)-14cos(x) is Minimum(2pin,-14),Maximum(pi+2pin,14)