Find (by hand) the intervals where the function is increasing and decreasing. Use this information to determine all local extrema and sketch a graph.
y = sinx + cosx
PLEASE HELP!! :(

Question

Find (by hand) the intervals where the function is increasing and decreasing. Use this information to determine all local extrema and sketch a graph.
y = sinx + cosx 
PLEASE HELP!! :(

campbell_st · Answer

well my suggestion is to find the stationary points 

the reason is that stationary points, if they are turning points have a zero gradient so the aren't increasing or decreasing. 

 test either side of the stationary points by substituting a value to see if the slope of the tangent is positive or negative... 

hope it makes sense

fibonaccichick666 · Answer

@vlfans1206 , do you know how to find the stationary points(critical points)?

campbell_st · Answer

the curve is periodic so then it is easier to find them information between 0 and 2 pi... then use the general solutions

fibonaccichick666 · Answer

yea, I was thinking that too, since most of us have sine and cosine memorized a less rigorous approach would be easier

anonymous · Answer

I have no idea how to find the critical points of this. That's the only problem I have

campbell_st · Answer

have you done calculus..?

anonymous · Answer

Yes, but I don't know how to solve critical numbers for Trigonomic things

anonymous · Answer

I know you set it equal to zero, but dont know where to go form there

fibonaccichick666 · Answer

you set the derivative equal to zero *

campbell_st · Answer

ok... so what did you get as the 1st derivative..?

anonymous · Answer

Cos x - sin x right?

campbell_st · Answer

great so set it to zero 

cos(x) - sin(x) = 0

what values can x take...?

campbell_st · Answer

keep it simple and restrict the domain to 0 to 2pi

anonymous · Answer

OH! Pi/2..?

fibonaccichick666 · Answer

double check that

fibonaccichick666 · Answer

what is cos pi/2?

campbell_st · Answer

not quite

if I rewrite it as 

cos(x) = sin(x)

anonymous · Answer

pi/4

campbell_st · Answer

that's correct... and there is another one in the 3rd quadrant... what would it be...?

anonymous · Answer

5pi/4 !

anonymous · Answer

I'm terrible at math, sorry :(

fibonaccichick666 · Answer

don't say that, you will become bad if you do! but anyways, yes 5pi/4,so now, you have your critical points on [0,2pi], now, you need to figure out if the graph is increasing or decreasing between those, do you know how?

anonymous · Answer

You can do the line check thing where you find a number lower than 0 and plug it into the first derivative and if the answer is negative,, its decreasing and if positive, its increasing. Right? and then same for a number between 0 adn 2pi and a number greater than 2pi

campbell_st · Answer

ok... so thats great   

so you determine increasing and decreasing choose values chose to the stationary  points

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