What is the extreme f(x)=25x-50sin(x),(-pi/4 , pi/2) ?

The extreme f(x)=25x-50sin(x),(-pi/4 , pi/2) is Minimum(pi/3 ,(25pi)/3-25sqrt(3))

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extreme f(x)=25x-50sin(x),(-pi/4 , pi/2)

extreme points

f (x) = 25 x - 50 sin (x), (- \frac{π}{4}, \frac{π}{2})

Minimum (\frac{π}{3}, \frac{25 π}{3} - 253)

Solution steps

Find the critical points:

x = \frac{π}{3}

Domain of

25 x - 50 sin (x), (- \frac{π}{4}, \frac{π}{2}) : - \frac{π}{4} < x < \frac{π}{2}

Find intervals:

Decreasing

: - \frac{π}{4} < x < \frac{π}{3},

Increasing

: \frac{π}{3} < x < \frac{π}{2}

Plug the extreme point

x = \frac{π}{3}

into

25 x - 50 sin (x) \Rightarrow y = \frac{25 π}{3} - 253

Minimum (\frac{π}{3}, \frac{25 π}{3} - 253)

f (x, y) = - 6 x^{2} + 5 y^{2} + 12 x - 20 y - 18

x - x

f (t) = 135 t - 5 t^{3}, - 4 \leq t \leq \infty

f (x) = 2 x^{3} - 4 x + 4

P (x, y) = 2 x + y

What is the extreme f(x)=25x-50sin(x),(-pi/4 , pi/2) ?
The extreme f(x)=25x-50sin(x),(-pi/4 , pi/2) is Minimum(pi/3 ,(25pi)/3-25sqrt(3))