What is the extreme f(x)=-5/2 sin(1/2 x) ?

The extreme f(x)=-5/2 sin(1/2 x) is Minimum(pi+4pin,-5/2),Maximum(3pi+4pin, 5/2)

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extreme f(x)=-5/2 sin(1/2 x)

extreme points

f (x) = - \frac{5}{2} sin (\frac{1}{2} x)

Minimum (π + 4 πn, - \frac{5}{2}), Maximum (3 π + 4 πn, \frac{5}{2})

Solution steps

Find the critical points:

x = π + 4 πn, x = 3 π + 4 πn

Domain of

- \frac{5}{2} sin (\frac{1}{2} x) : - \infty < x < \infty

Find intervals:

Decreasing

: 4 πn \leq x < π + 4 πn,

Increasing

: π + 4 πn < x < 3 π + 4 πn,

Decreasing

: 3 π + 4 πn < x < 4 π + 4 πn

Plug the extreme point

x = π + 4 πn

into

- \frac{5}{2} sin (\frac{1}{2} x) \Rightarrow y = - \frac{5}{2}

Minimum (π + 4 πn, - \frac{5}{2})

Plug the extreme point

x = 3 π + 4 πn

into

- \frac{5}{2} sin (\frac{1}{2} x) \Rightarrow y = \frac{5}{2}

Maximum (3 π + 4 πn, \frac{5}{2})

Minimum (π + 4 πn, - \frac{5}{2}), Maximum (3 π + 4 πn, \frac{5}{2})

f (x) = x^{2} + 7 x - 1

f (x) = - 3 x^{3} + 3 x^{2} - x - 5

5 x^{\frac{2}{3}} - x^{\frac{1}{3}}

2 sin^{2} (x)

f (x, y) = x^{2} + x - 3 x y + y^{3} - 5

What is the extreme f(x)=-5/2 sin(1/2 x) ?
The extreme f(x)=-5/2 sin(1/2 x) is Minimum(pi+4pin,-5/2),Maximum(3pi+4pin, 5/2)