- #1

DryRun

Gold Member

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- 4

**Homework Statement**

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.