Question

critic numbers of f(x) = sinx + cos x ?

Answer 1

The critical numbers of a function are the values of x for which the derivative is 0 or undefined. So, we first need to take the derivative, which you should find is:
\[f \prime (x)=\cos x - \sin x\] There are no values for which this function is undefined, so we need to set it equal to 0:
\[\cos x - \sin x =0\]Add sinx to both sides and you get:
\[\cos x=\sin x\] You could solve this either by graphing the two and finding intersections, or if you've memorized a trig table, use that to help you. When you solve this system you'll have the critical values.

Answer 2

so the critic numbers of that function are the values for x where cos x = sin x ?

Answer 3

Yep, exactly.

Answer 4

any help with that equation?

Answer 5

I would graph the two and find their intersections, I don't have my graphing calculator on me right now.

Answer 6

no problem, i don't think i need it for this problem. thanks!

Answer 7

starting with
\[ \cos x=\sin x \]
if you divide by cos x you get
\[ 1 = \frac{\sin x}{\cos x} \\ 1 = \tan x \]
so you want all angles where tan x = 1