Is #f(x)= cos(x+(5pi)/4) # increasing or decreasing at #x=pi/4 #?
1 Answer
Jul 9, 2018
See explanation.
Explanation:
Generally if the function

#f(x)# is increasing at#x_0# if#f^'(x_0)>0# 
#f(x)# is decreasing at#x_0# if#f^'(x_0)<0# 
#f^'(x)# may have an extremum at#x_0# if#f^'(x_0)=0# (additional test is required)
In the given example we have:
To check if the point is extremum we have to check if the first derivative changes sign at
graph{(y+sin(x+(5pi)/4))((x+pi/4)^2+(y^2)0.01)=0 [4, 4, 2, 2]}
At