find a point c satisfying the conclusion of the Mean Value Theorem for the given function and interval y=cosx-sinx [0,2pi]

Question

tayfishb · Answer

$$f \prime c=\frac{ f(b)-f(a) }{ b-a }$$

tayfishb · Answer

$$f \prime x=-sinx-cosx$$

tayfishb · Answer

$$\frac{ (-\cos2\pi -\sin2\pi )-(\cos 0-\sin 0) }{2\pi -0 }$$

tayfishb · Answer

$$\frac{ (1-0)-(1-0) }{ 2\pi -0}=\frac{ 0 }{ 2 \pi  }$$

tayfishb · Answer

$$0=-sinx-cosx$$

tayfishb · Answer

$$sinx=-cosx$$

tayfishb · Answer

now what?????

tayfishb · Answer

@mathmale @TheSmartOne

nnesha · Answer

divide both sides by -cosx

tayfishb · Answer

$$-tanx=1???$$

nnesha · Answer

yes solve for tanx
and then use the unit circle to find where tanx = -1

nnesha · Answer

$$\frac{\color{Red}{-} \cos 2\pi - \sin 2\pi  }{ 2\pi -0  }$$
`-` is a typo i guess

tayfishb · Answer

but arent there two answers for that? second and fourth quadrant?

nnesha · Answer

yes.

tayfishb · Answer

so $$x=\frac{ \sqrt{2} }{ 2}$$?

tayfishb · Answer

no wait nevermind i got it

nnesha · Answer

hmm in other words you're solving for x
to find an angle you should take invs of trig ratio

so x= arctan(-1) 
sqrt{2}/2 is just the x-coordinate /y-coordinate the tanx 
tanx=sinx/cosx

so basically you have to find at what degree/radian tanx=-1

nnesha · Answer

x-coordinate /y-coordinate NOT  the tanx **

tayfishb · Answer

yeah i got it, its $$\frac{ 7\pi }{ 4 }$$

tayfishb · Answer

thank you sooo much

nnesha · Answer

what about  the other one there are two right ??
b/w [0,2pi]

tayfishb · Answer

my textbook answers said only the 7pi/4 was correct