Question

Find the maximum and minimum values, if any, of the following functions given by (i) f(x) = (2x − 1)² + 3 (ii) f(x) = 9x²+12x+2 (iii) f(x) = −(x − 1)²+ 10 (iv) g(x) = x³ +1

Answer 1

The given function is f(x) = (2x − 1)² + 3. It can be observed that (2x − 1)² ≥ 0 for every x ∴ R. Therefore, f(x) = (2x − 1)²+3 ≥ 3 for every x ∴ R. The minimum value of f is attained when 2x − 1 = 0.

3x + 2 = 0 ∴ x=\(-\frac{2}{3}\)

∴The minimum value of f = f(\(-\frac{2}{3}\))=(3(\(-\frac{2}{3}\))+2)²

Hence, function f does not have a maximum value.

The given function is f(x) =−(x−1)²+10.

It can be observed that (x − 1) 2 ≥ 0 for every x ∴ R.