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

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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
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  • #2
nrqed
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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)?
 
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  • #3
osilmag
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Help, you could use the product rule, then set it equal to zero.
 
  • #4
vela
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Homework Statement:: help with my work
Relevant Equations:: derivative and integral

the maximum value would not be making the derivative equal to zero? would it be x = 1? I did not understand
The maximum value might be attained at a critical point or at the endpoints of the closed interval.

Try plotting the function for a few values of ##n## to get an idea of what you should get.
 

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