Question

Determine the points of maxima and minima of the function f(x) = 1/8log x – bx + x², x > 0 where b (≥ 0) is a constant.

Answer 1

Given f(x) = 1/8logx – bx + x², x > 0

⇒ f'(x) = 1/8x – b + 2x

For max or min, f'(x) gives 1/8x – b + 2x = 0

⇒ 16x² – 8bx + 1 = 0

Clearly, root is real, if b ≥ 1

Thus, x = (b – √(b² – 1))/b is the point of maxima and x =(b + √(b² – 1))/b is the point of minima.