Question 38 of 82beginner🔧 ApplyShort Answer4 marks
Find the maximum and minimum values, if any, of the following functions given by
(i)
f(x) = (2x - 1)² + 3
Answer
Minimum value = 3 at x = 1/2; No maximum value
(ii)
f(x) = 9x² + 12x + 2
Answer
Minimum value = -2 at x = -2/3; No maximum value
(iii)
f(x) = -(x - 1)² + 10
Answer
Maximum value = 10 at x = 1; No minimum value
(iv)
g(x) = x³ + 1
Answer
Neither maximum nor minimum value
Explanation
This question tests understanding of finding maxima/minima using algebraic properties. For quadratic functions, completing the square helps identify the vertex. When the coefficient of squared term is positive, parabola opens upward giving a minimum. When negative, parabola opens downward giving a maximum. Cubic functions like x³ + 1 have no global maxima or minima as they extend to ±∞.