A community for students.
Here's the question you clicked on:
 0 viewing
shubhamsrg
 3 years ago
how to prove :
sin^3 x + cos ^3 x <= 1
shubhamsrg
 3 years ago
how to prove : sin^3 x + cos ^3 x <= 1

This Question is Closed

NewbieCarrot
 3 years ago
Best ResponseYou've already chosen the best response.1Did you learn integration before?

NewbieCarrot
 3 years ago
Best ResponseYou've already chosen the best response.1Use integration to find the critical points and take that back to your equation sin^3(x)+cos^3(x). But I think it should be not less than 1

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0didnt get you..please elaborate ..

NewbieCarrot
 3 years ago
Best ResponseYou've already chosen the best response.1let f(x)=sin^3(x)+cos^3(x), then f'(x)=3sin^2(x)cos(x)3cos^2(x)sin(x) and solve f'(x)=0 for x and use x to find the maximum or minimum of f(x).

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0fair enough i guess.. i got x=0,pi/2 and pi/4 0 and pi/2 yield f(x) =1 and the other one gives 1/sqrt(2) seems correct !! hmm..

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0in the mean time,,i came across this : we know sin^2x ( sinx 1) <= cos^2x ( 1 cosx) equality will hold for x=0 or pi/2 so, sin^3 x  sin^2 x <= cos^2x  cos^3x => sin^3x + cos^3 c <= 1 !!!!!!!!!!!!!!!!!

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0thanks,,@NewbieCarrot
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.