Find the maximum and the minimum values, if any, without using derivatives of the functions f (x) = –(x – 1)2 + 2 on R

Asked by Sakshi | 1 year ago |  76

##### Solution :-

Given f(x) = – (x – 1)2 + 2

It can be observed that (x – 1)≥ 0 for every x ∈ R

Therefore, f(x) = – (x – 1)2 + 2 ≤ 2 for every x ∈ R

The maximum value of f is attained when (x – 1) = 0

(x – 1) = 0, x = 1

Since, Maximum value of f = f (1) = – (1 – 1)2 + 2 = 2

Hence, function f does not have minimum value.

Answered by Aaryan | 1 year ago

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