Find the maximum and the minimum values, if any, without using derivatives of the following functions:

Question

Find the maximum and the minimum values, if any, without using derivatives of the following functions: f(x) = – |x + 1| + 3 on R

Philoid · Accepted Answer

We know that – |x + 1| ≤ 0 for every x ∈ R.

Therefore, g(x) = – |x + 1| + 3 ≤ 3 for every x ∈ R.

The maximum value of g is attained when |x + 1| = 0

|x + 1| = 0

x = – 1

Since, Maximum Value of g = g( – 1) = – | – 1 + 1| + 3 = 3

Hence, function g does not have minimum value.