How to find the absolute max and min for 2cos(t)+sin(2t), calculus 1 tutorial

To find the absolute minimum and maximum of f(t)=2cos(t)+sin(2t) on [0, pi/2], we will have to find all the critical numbers of the function on the given interval, then we check the value of the function at the critical numbers and also the endpoints.
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[@crystalhasley7613]

thanks for such clear and precise instruction, obvious patience for explaining every step

[@JACdUpProductions]

absolutely amazing way of explaining every single thing. thank you so much. liked and subscribed

[@officiallyaninja]

whoa, what's the tic tac toe method? I've never seen that

[@littleretroship6403]

I want to try this. For the record, I have no experience finding absolute mins and maxes with trig functions.I feel like it’s gonna be hard but i want a challenge.
f’(t)= -2sint + 2cos(2t)
set f’(t) to 0 and solve for t
0=-2sint + 2cos(2t)
I can factor out both -2 and 2
0=2(-sint + cos(2t))
0=-2(sint - cos(2t))
And ig divide both sides
0=cos(2t) - sint
0=sint - cos(2t)
I’m sorry but I have no clue how to solve when it’s sint and cos(2t) I will check wolfram alpha
Nevermind this is really complicated
Edit: ah so I did have to have the same input. I don’t know any of those identities. Thanks for teaching me, now I know!
Wow the tic tac toe method looks useful!

[@oom_boudewijns6920]

Just go to highschool :)

[@littleretroship6403]

@@oom_boudewijns6920 too young

[@oom_boudewijns6920]

@@littleretroship6403 wowwww, average ppl get taught funxtions with sinus in the 10th grade!!!

[@TheEc1ypse]

@@oom_boudewijns6920 ya but getting max and mins is gr 12 calc

[@Greem877]

So we basically have to just differentiate the equation then use those critical points to find out the values on the critical points then we will use the extreme point of intervals to determine which one is the maximum or the minimum