A community for students.
Here's the question you clicked on:
 0 viewing
 3 years ago
If a and b are positive numbers, find the maximum value of f(x)=x^a*(1x)^b, 0 less than or equal to x less than or equal to 1.
Your answer may depend on a and b. What is the maximum value?
 3 years ago
If a and b are positive numbers, find the maximum value of f(x)=x^a*(1x)^b, 0 less than or equal to x less than or equal to 1. Your answer may depend on a and b. What is the maximum value?

This Question is Closed

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1maximum value of: \[f(x)=x^a*(1x)^b;\ 0\le x \le 1\]

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1\[f'(x)=ax^{(a1)}(1x)^bx^ab(1x)^{(b1)}\] \[ax^{(a1)}(1x)^bx^ab(1x)^{(b1)}=0\] solving this might get us some critical points

moneybird
 3 years ago
Best ResponseYou've already chosen the best response.3Critical point = a/(a+b)?

moneybird
 3 years ago
Best ResponseYou've already chosen the best response.3Got the answer. It is (a/(a+b))^a(b/(a+b))^b

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1\[ax^{(a1)}(1x)^b=x^ab(1x)^{(b1)}\] \[ax^{(a1)}x^{a}(1x)^b=b(1x)^{(b1)}\] \[ax^{1}(1x)^b=b(1x)^{(b1)}\] \[a=xb(1x)^{(b1)}(1x)^{b}\] \[a=xb(1x)^{1}\] \[\frac{a}{b}=\frac{x}{1x}\] \[aax=bx\] \[a=bx+ax\] \[\frac{a}{b+a}=x\] looks to be that way if i did it right
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.