Question

F(x,y) =sinx + siny + sin(x+ y) 
find the critical points of the local max and min

im kinda stuck on this one, please help?

Answer 1

to find the critical point you need to equate first derivative to zero.

Answer 2

both partials need to be 0

Answer 3

do it simultaneously ... you'll have a system of two equations in x and y. solve for x and y

Answer 4

well yeah i knw how to do that already
fx=cosx+cos(x+y)
fy=cosy+cos(x+y)

Answer 5

idk how to solve for x and y tho

Answer 6

so what are the critical points?

Answer 7

thats wht im looking for

Answer 8

This is a function of x and y, it's a surface in R3

Answer 9

LOL i dont need u to explain that to me i knw that already i just need to knw how to solve for x and y to find the critical points

Answer 10

if you knw how to do that could u please tell me? cuz it seems difficult to isolate X or Y by its self with this function

Answer 11

perhaps we can use cramer's rule here?

Answer 12

i forgot how to do that

Answer 13

http://tutorial.math.lamar.edu/Classes/LinAlg/CramersRule.aspx

Answer 14

hmm ... what do we get here?

use cos D + cos C = 0