# Differentiate f(x)=x(1-x)^n

Homework Statement:
help with my work
Relevant Equations:
derivative and integral
Hello, good afternoon guys. I need a little help from you: D

1)n a positive integer.
f(x)=x(1-x)^n
Solve the equation f'(x)=0 in 0<x<1

this question I asked and found x = 1 / (x + 1) ok

2)An be the maximum value of f(x)=x(1-x)^n in [0,1]
Calculate lim (n+1)an
n tending to infinity

the maximum value would not be making the derivative equal to zero? would it be x = 1? I did not understand Last edited by a moderator:

nrqed
Homework Helper
Gold Member
Homework Statement:: help with my work
Relevant Equations:: derivative and integral

Hello, good afternoon guys. I need a little help from you: D

1)n a positive integer.
f(x)=x(1-x)^n
Solve the equation f'(x)=0 in 0<x<1

this question I asked and found x = 1 / (x + 1) ok

2)An be the maximum value of f(x)=x(1-x)^n in [0,1]
Calculate lim (n+1)an
n tending to infinity

the maximum value would not be making the derivative equal to zero? would it be x = 1? I did not understand View attachment 264068
You did not do the first part correctly.

What is the derivative f'(x)?

• Delta2 and member 587159
osilmag
Gold Member
Help, you could use the product rule, then set it equal to zero.

vela
Staff Emeritus