How do you find the local maximum of y= -3cos(x-(pi/4))?

Question

This must be done algebraically, without a calculator.
How do I find the point without a calculator?
Steps would be lovely and not just the answer.

Answer 1

Well...

A local maximum of -cosx is the same as the local minimum of cosx.

A local minimum of cos x is at x = &pi .

A local minimum of cos(x - &pi/4) is at x = 5&pi/4.
[since x - &pi/4 = &pi when x = 5&pi/4]

Hence the local maximum of y= -3cos(x - &pi/4) is at x = 5&pi/4 and the value of the function at that point is 3.

=> point (5&pi/4, 3)

Hope this helps.

Answer 2

y= -3cos(x-(pi/4))

y'=0
3sin(x-(pi/4))=0
sin(x-(pi/4))=0
x-pi/4=0
x=pi/4 y=-3 min value

x-pi/4=pi
x=5pi/4 put this value in the function
y=3
max value

max point(5pi/4,3)