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 onlyB. 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].]
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.]
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