Find the maximum and the minimum values, if any, without using derivatives of the functions f (x) = 4x2 – 4x + 4 on R

Asked by Sakshi | 1 year ago |  125

1 Answer

Solution :-

Given f (x) = 4x2 – 4x + 4 on R

= 4x2 – 4x + 1 + 3

By grouping the above equation we get,

= (2x – 1)2 + 3

Since, (2x – 1)2 ≥ 0

= (2x – 1)2 + 3 ≥ 3

= $$f(x) ≥ f (\dfrac{1}{2})$$

Thus, the minimum value of f(x) is 3 at x = $$\dfrac{1}{2}$$

Since, f(x) can be made large. Therefore maximum value does not exist.

Answered by Sakshi | 1 year ago

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