What is the extreme f(x)=-5sin(x)cos(x) ?

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

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extreme f(x)=-5sin(x)cos(x)

extreme points

f (x) = - 5 sin (x) cos (x)

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

Solution steps

Find the critical points:

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Domain of

- 5 sin (x) cos (x) : - \infty < x < \infty

Find intervals:

Decreasing

: πn \leq x < \frac{π}{4} + πn,

Increasing

: \frac{π}{4} + πn < x < \frac{3 π}{4} + πn,

Decreasing

: \frac{3 π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

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

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

Plug the extreme point

x = \frac{3 π}{4} + πn

into

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

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

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

x^{4} + 8 x^{3}

f (x) = x^{2} - 9 x

f (x) = (\frac{e ^{x}}{7 + e ^{x}})

f (x) = 6 x^{2} - 12

\frac{4 x - ln ( 3 x )}{x}

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