# Another Curve Sketching question

• Jan 6th 2008, 03:49 PM
pbfan12
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.
• Jan 6th 2008, 04:01 PM
mr fantastic
Quote:

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?