Find the maximum or minimum value, if any, without using derivatives,

1.	Find the maximum or minimum value, if any, without using derivatives, of the function: –\|x + 4\| + 6
Answer» We can write it as \|x + 4\| ≥ 0 By taking – ve sign – \|x + 4\| ≤ 0 By adding 6 on both sides – (x + 4) + 6 ≤ 0 + 6 Where f (x) ≤ 6 Here the maximum value of f (x) = 6 which occurs at x = – 4 which is the point of absolute maxima and minimum value of f (x) does not exists.

Find the maximum or minimum value, if any, without using derivatives, of the function: –|x + 4| + 6

Answer»

We can write it as

|x + 4| ≥ 0

By taking – ve sign

– |x + 4| ≤ 0

By adding 6 on both sides

– (x + 4) + 6 ≤ 0 + 6

Where f (x) ≤ 6

Here the maximum value of f (x) = 6 which occurs at x = – 4 which is the point of absolute maxima and minimum value of f (x) does not exists.