Question

I have set the derivative to zero, and i got this
cosx=sinx. Now i am asked to find all the critical points, i know one of the is pi/4 since both sides of the equation are equal then, but how come the other one the book gives me is 5pi/4. can somone clarify?

Answer 1

In order to find critical points. You must solve for x. Values of x are your critical points

Answer 2

Okay, so i found 1 which is pi/4 but how is 5pi/4 the other one?

Answer 3

pi/4 = 45 degrees
5pi/4 = 225 degrees
both satisfy the equation

i prefer degrres to radians

Answer 4

but isnt 225 degrees located in the 3rd quadrent of the unit circle?

Answer 5

yes the equation simplifies to tan x = 1
and tan is positive in 1st and 3rd quadrants

Answer 6

When you solve for x, you are solving for angles that have the same trig function. 225 is 45 degrees away from 180, and that fact, without going into more detail is the connection.

Answer 7

right. Can i ask you one other question. The original function was (x/2)+cosx, and i found the critical point of pi/6, how do i do the computation inorder to find the y value of the max

Answer 8

It is difficult to work in the middle, post the whole question in a new post.

Answer 9

good idea - i'm a little confused at this point!