Question

the function f(x) = sin(cosx) is increasing if

Answer 1

Step-by-step explanation:

Given,

f(x)=sinx−cosx, where 0<x<2π

f  

′

(x)=cosx+sinx

for critical points, put f  

′

(x)=0

i.e. cosx+sinx=0

tanx=−1

x=  

4

3π

​

,  

4

7π

​

 

clearly, f  

′

(x)>0 if 0<x<  

4

3π

​

&  

4

7π

​

<x<2π

f  

′

(x)<0 if  

4

3π

​

<x<  

4

7π

​

 

Thus, f(x) increases in (0,  

4

3π

​

)∪(  

4

7π

​

,2π), decreases in (  

4

3π

​

,  

4

7π

​

)