Question

8. Find the maximum value of (sin-1 x)cube + (cos-1 x)cube​

Answer 1

Answer:

INVERSE TRIGONOMETRIC FUNCTIONS & APPLICATION OF DERIVATIVES  :D 

Final Answer : Min. Value :    

                        Max . Value :  

STEPS: 

1)   Let 

 

Now ,Find below points as your own or take it as your Homework  which is trivial 

Critical Points / Boundary Points : 

 

 2)  Since we know ,

arcsin(1) = pi/2 , arcsin(1/root(2)) = pi/4 

arccos(-1) =pi   ,  arccos(1/root(2)) = pi/4 

Substitute these values in  f(x) , to get   

 f(-1) =    

   f(1)  =   

  f(1/root(2))  =  

3) Hence , looking above values :

Max f(x)  =   

Min f(x)    =    

Domain  :