Question

What is the absolute maximum of the function |x – 3| in the interval [4, 5]?

Answer 1

Answer:

x-3 45

Step-by-step explanation:

answer is 1, 2yt hshhshshshs

Answer 2

Given:

A function |x - 3|.

To Find:

The maximum value of the function in the interval [ 4, 5 ].

Solution:

1. The given function is | x- 3 |.

2. The modulus of a number is defined as an absolute value of a number, irrespective of the sign of the number. it is denoted by | |.

Example: modulus of -1, and 1, i.e | -1 | and | 1 | is 1.

3. The mentioned interval is [ 4, 5 ].

• The value of the given function at x = 4  is | 4 - 3 | = +1.
• The value of the given function at x = 4.1 is | 4.1 - 3| = + 1.1
• The value of the given function at x = 4.2 is | 4.2 - 3 | = + 1.2.

4. The value of the given function is increasing as the value of X is increasing in the given interval.

• The function | x - 3 | is a decreasing function in the interval ( -∞ , 3)
• The function | x - 3| is an increasing function in the interval ( 3, ∞ )
• The mentioned interval [ 4, 5] lies in the increasing interval.

5. Therefore, the value of the function increases as the value of x is increasing in the interval [ 4, 5].

6. Therefore, the maximum value of the function is the value at x = 5.

=>  value of | x - 3 | at x = 5,

=> | 5 - 3 | = +2.

Therefore, the absolute maximum of the function in the given interval is +2.