(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

If λ is a positive constant, determine the maximum and minimum values of

f(x) = 9(4-3x^2)(λ-λ^-1-x)

and show that the difference between them is 4(λ+λ^-1)^3. Find the least value of this difference as the parameter λ is varied.

The attempt at a solution

I expanded the right-hand side and then did a first d.w.r.t.x

dy/dx = 81x^2 + 54x/λ - 54λx -36

I have to equate this to zero, to find either the minimum or maximum value:

81x^2 + 54x/λ - 54λx -36 = 0

But i don't know how to proceed next, since the value of λ is unknown, so i cannot solve for x.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Derivative of f(x) to find its maximum and minimum values

**Physics Forums | Science Articles, Homework Help, Discussion**