What is the extreme f(x)=x+sin^2(x) ?

The extreme f(x)=x+sin^2(x) is Saddle((3pi)/4+pin,(3pi)/4+pin+sin^2((3pi)/4+pin))

extreme f(x)=x+sin^2(x)

extreme points

f (x) = x + sin^{2} (x)

Saddle (\frac{3 π}{4} + πn, \frac{3 π}{4} + πn + sin^{2} (\frac{3 π}{4} + πn))

Solution steps

Find the critical points:

x = \frac{3 π}{4} + πn

Domain of

x + sin^{2} (x) : - \infty < x < \infty

Find intervals:

Increasing

: πn \leq x < \frac{3 π}{4} + πn,

Increasing

: \frac{3 π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{3 π}{4} + πn

into

x + sin^{2} (x) \Rightarrow y = \frac{3 π}{4} + πn + sin^{2} (\frac{3 π}{4} + πn)

Saddle (\frac{3 π}{4} + πn, \frac{3 π}{4} + πn + sin^{2} (\frac{3 π}{4} + πn))

2 x + 1 + \frac{5}{x - 5}

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

f (x) = \frac{1}{3} x^{3} - \frac{1}{2} x^{2}

x x^{2} + 25

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 2 x - 10 y

What is the extreme f(x)=x+sin^2(x) ?
The extreme f(x)=x+sin^2(x) is Saddle((3pi)/4+pin,(3pi)/4+pin+sin^2((3pi)/4+pin))