Maximum and Minimum Values

Definition of Maximum and Minimum Values

Maximum Value: The maximum value of a quadratic function f(x) = ax2 + bx + c where a < 0,="" is="" the="">y- coordinate of the vertex.

Minimum Value: The minimum value of a quadratic function f(x) = ax2 + bx + c where a > 0, is the y- coordinate of the vertex.

Examples of Maximum and Minimum Values

  • The quadratic function f(x) = 9 - x2 has the maximum value of 9.
  • The quadratic function f(x) = 16 + x2 has the minimum value of 16.

Video Examples: Maximum and Minimum Values of Sine and Cosine Functions, Ex 1


Solved Example on Maximum and Minimum Values

Ques: Which of the following statements are correct for the function
f(x) = (x - 3)(x + 2) on the interval [- 5, 2]?
1. f(x) has Maximum Value at x = - 5
2. f(x) has Minimum Value at x = 2
3. f(x) has Maximum Value at x = - 3
4. f(x) has Minimum Value at x = 0.5

    Choices:
    A. 2 and 3 only
    B. 1 and 3 only
    C. 2 and 4 only
    D. 1 and 4 only
    Correct Answer: D

Solution:

    Step 1: f(x) = (x - 3)(x + 2) [Write the function.]
    Step 2: [Draw the graph of f(x) on the interval [- 5, 2].]
     Example on   Maximum and Minimum Values
    Step 3: f(x) has Maximum Value at x = - 5. [From the graph.]
    Step 4: f(x) has Minimum Value at x = 0.5. [From the graph.]