Question

Solve the following question and mark the best possible option.
Find the maximum value of (1 – x) (1 + x) (1 + x) where x ≥ 0.

विकल्प

• `32/27`

• `12/31`

• `33/7`

• `7/33`

Answer 1

We have F(x) = (1 - x)(1 + x)(1 + x)

= `1/2` x 2(1 - x)(1 + x)(1 + x)

= `1/2(2 - 2x)(1 + x)(1 + x) ≤ 1/2[(2 - 2x + 1 + x + 1 + x)/(3)]^3 ["AM" ≥ "GM"]`

= `1/2(4/3)^3 = 32/27`

∴ f(x) ≤ `32/27`

Hence maximum value of (1 - x)(1 + x)(1 + x) is `32/27`