Find the critical numbers of 2cos(x)+sin^2(x)

Find the critical numbers of 2cos(x)+sin^2(x),

This problem is from Single Variable Calculus, by James Stewart,

blackpenredpen

calculus 1 derivative,
blackpenredpen calculus,
calculus tutorial,

[abstractcafe]

I hate when those critical numbers overly examine my performance in math.

[georgeimus]

even 5 years later this video saves students like me. thank you for your excellent teaching style

[alvinromero]

Man you never know how many people you have save from crippling depression! <3

[quahntasy]

Thank you for making these types of videos. Love it.

I have never been this early though.

[malirk]

Thank you for all your hard work creating math educational videos!

[joshdilworth]

I think a video for finding the critical numbers of a function where the function value itself is a value of another function, would be interesting; something to the effect of:
cos(x)/x = ln(1 + f(x)^2)

[BigRedProductions]

You should totally add up all the Riemann Zeta function values, starting from the 3rd term. It’s super cool, I did it already. It’s so strange that we can’t even define like any odd inputs but we can add all of them together

[fernandovalner]

so simple and well explained, very good.

[xaxuser]

I think the views of your amazing chanel are going down i don t know why but i think cz the newest videos are not about number theory, numbers games and fun maths because that s what we want and nice video btw #yaaaayy

[anthonytam]

BPRP! Could you please make an introductory video to all of the trig functions for us all pre-calc students? ❤️ #YAY

[tofu]

a math problem a day keeps the alzheimer away

[andrewhoban]

I love your videos. Very very helpful. As my calc three course has gone on though, I have not been able to find your exact right videos. I wish I could but since I can't I'm gravitating to other youtubers. I wish I could find your explanation of finding critical points for a system of ODE's!

[winterrain]

#YAY ; Find coefficients of a cubic equation such that the elliptic curve has an infinite number of rational solutions. y^2= Ax^3+ Bx^2+Cx+D

[rimanbachar]

INTEGRAL OF.

(x^2 )/ (xsinx + cosx) ^2

[yihangzhu]

I noticed that d(sin^2 x)/dx = 2 * sin x * d(sin x)/dx = sin(2*x). So how can I solve the equation that 2 * y(x) * dy/dx = y(2*x) ? Is "y(x) = sin x" the only solution?

[appley]

2 cos x + sin^2 x
= - cos^2 x + 2 cos x + 1
= -( cos x - 1)^2 + 2
Knowing that - 1 <= cos x <= 1,
maximum is 2 occuring at cos x = 1, i.e. x = 0, +- 2 pi, ...
minimum is 1 occuring at cos x = 0, i.e. x = +- pi, +- 3 pi, ...

[husklyman]

In one of your videos you said you will find the derivative of x^x^x... n times, where this video is?

[nlain]

This was a great calc 1 review, thanks! I need this since I don't wanna be rusty when I start calc 3 next semester
How would you go about finding local minima and maxima from there? It's the sign of the second derivative, right?

[Pterryreal]

Interesting that you never use the according symbols for this kind of solutions.

I am used to write this instead:
θ = kπ ; k ∈ ℤ
In my opinion it is clearer and on the point.

But okay, it is roughly the same. Maybe using an "n" is not a good idea because it symbolize most of the times the natural numbers and not the integers. You know for consistency reasons, like the triangles ;)

[darielfarfan]

Porfavor integra esto ( (x^2+1+ sqrt( x^2 + x + 1)/( x^3 + x^2 * sqrt( x^2 + x + 1) ))*dx . Lo llevo intentando mucho tiempo y no me sale. Saludos desde Perú . Me gustan tus vídeos 😀😊