Math Help - Another Curve Sketching question

1. Another Curve Sketching question

Hi, sorry to post another question about curve sketching (this is my last one) but I am having difficulties with the following function:

f(x) = cosx - sinx

If someone could provide a sketch of what this function looks like that would be great, that way I have something to work towards. I've done all the calculus work but I'm having a real hard time making sense of it.

I have:

- the y-int: y=1
- the zeros: x=(pi)/4 and 5(pi)/4
- niether odd or even
- no asymptotes
- increasing everywhere (I'm really not sure if that is right)
- no local max/min
- concave down everywhere (I'm also not sure if that is right)
- no inflection points

I've had no luck graphing this so I'm sure I've made a big mistake somewhere. Any help at all would be great!

Thanks.

2. Originally Posted by pbfan12
Hi, sorry to post another question about curve sketching (this is my last one) but I am having difficulties with the following function:

f(x) = cosx - sinx

If someone could provide a sketch of what this function looks like that would be great, that way I have something to work towards. I've done all the calculus work but I'm having a real hard time making sense of it.

I have:

- the y-int: y=1 Mr F says: Correct

- the zeros: x=(pi)/4 and 5(pi)/4 Mr F says: Partly correct .... You can obviously add multiples of $2 \pi$ to each of these to get more zeros.

- niether odd or even Mr F says: Correct

- no asymptotes Mr F says: Correct

- increasing everywhere (I'm really not sure if that is right)

- no local max/min Mr F says: Wrong. How did you arrive at this conclusion? $f^{'} (x) = 0$ has an infinite number of solutions .......

- concave down everywhere (I'm also not sure if that is right) Mr F says: It's not.

- no inflection points Mr F says: Wrong. How did you arrive at this conclusion?

I've had no luck graphing this so I'm sure I've made a big mistake somewhere. Any help at all would be great!

Thanks.
You should also consider that the domain is R and the range is .....?

Life will be much much much easier for you if you express cosx - sinx in the form $Acos(x - \phi)$. Do you know how to do this?