Question

F(x) = sin2x+x , -pi/2 <x<pi/2

find local maximum and minimum​

Answer 1

Answer:

(x)=sin2x−x, −

2

π

≤x≤

2

π

f

′

(x)=2cos2x−1 −π/2≤x≤π/2

⇒f

′

(x)=0 −π2x≤π

⇒2cos2x−1=0

cos2x=

2

1

∴2x=

3

π

,

3

−π

x=

6

π

,

6

−π

at x=

6

π

,f(x) has local maximum

f(

6

π

)=sin(

3

π

)−

6

π

=

2

3

−

6

π

at x=−

6

π

,f(x) has local minima

f(

6

−π

)=sin(−

3

π

)+

6

π

=

6

π

−

2

3