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

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

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

Increasing

: πn \leq x < \frac{π}{4} + πn,

Decreasing

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

Increasing

: \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}

Maximum (\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}

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

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

f (x, y) = x^{4} + y^{2} - 2 x^{2} - 5

f (x) = x + \frac{3}{x}

f (x) = \frac{x}{25 + x ^{2}}

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

f (x) = x^{2} - 4 x + 9

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