Find the values of p so that the function 8sin^3(x)=p-7cos2x would not have any solutions.

Question

experimentx · Answer

8sin^3(x) will always be less or equal than 8 and greater than or equal to -8, since sine function will always generate less than
7cos2x will always be less than or equal to 7 and greater than or equal to -7, 
so, 

if p < -15 then it will not have any solution

and also if p > 15, same is the case.

anonymous · Answer

But I've given the answer and it's supposed to be p=(-inf;-15)u(7;inf)

anonymous · Answer

How do you get the 7 to infinity part?

anonymous · Answer

Got it. Thanks!

experimentx · Answer

(-inf;-15)u(15;inf) is my answer

anonymous · Answer

Yes, mine must be wrong.

experimentx · Answer

incase cos part is -7 and the sin part is 8, than p must be 15, if p is greater than 15, then no solution exist.

anonymous · Answer

Yes.

experimentx · Answer

Oo... wait, maximize and minimize the following function, you will get a lot better answer
f(x) = 8sin^3(x)-7cos2x

anonymous · Answer

How do you do that?

experimentx · Answer

take first derivative ... and equate it to zero. and solve for x.
for now!! and alert me

anonymous · Answer

Okay. I'll let you know.

anonymous · Answer

x=nPi , x=2nPi , x=(-1)^n+nPi

anonymous · Answer

Second one is wrong.

anonymous · Answer

+-Pi/2+2nPi.

experimentx · Answer

let's see http://www.wolframalpha.com/input/?i=+y+%3D+8sin%5E3%28x%29-7cos2x+

experimentx · Answer

http://www4c.wolframalpha.com/Calculate/MSP/MSP43821a11302d5f30bd4f00001ghb080f5h89969g?MSPStoreType=image/gif&s=54&w=372&h=36

anonymous · Answer

Yes, got those already.

experimentx · Answer

http://www.wolframalpha.com/input/?i=solve+14%28sin2x%29%2B24+%28sinx%29%5E2+cosx

experimentx · Answer

in these points you either get maximum value or minimum value

anonymous · Answer

And then?

experimentx · Answer

the best way would be to put these values in our function and check which gives maximum value and which gives minimum value

experimentx · Answer

beyond greatest maximum value, solution does not exist .... and same goes to minimum value

anonymous · Answer

Alright. I try to write it all down. Thank you!

experimentx · Answer

and your answer is p<-7 and p>15

experimentx · Answer

thats from graph

anonymous · Answer

Oh, okay.

experimentx · Answer

http://www4c.wolframalpha.com/Calculate/MSP/MSP66131a112fh7c8a5gf7b00006276ff9g8beb6fif?MSPStoreType=image/gif&s=56&w=299&h=128&cdf=RangeControl