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Find the Maximum and Minimum Values, If Any, of the Following Functions Given by F(X) = (2x − 1)2 + 3 - Mathematics

Find the maximum and minimum values, if any, of the following functions given by

f(x) = (2x − 1)2 + 3 

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Solution

The given function is f(x) = (2x − 1)2 + 3.

It can be observed that (2− 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.

Hence, function f does not have a maximum value.

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APPEARS IN

NCERT Class 12 Maths
Chapter 6 Application of Derivatives
Q 1.1 | Page 231
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