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 – 3)2 + 9
Answer» It is given that f (x) = – (x – 3)² + 9 Here (x – 3)² ≥ 0 We can write it as – (x – 3)² ≤ 0 By adding 9 on both sides – (x – 3)² + 9 ≤ 0 + 9 Where f (x) ≤ 9 So the maximum value of f (x) = 9 which occurs at x = 3 which is the point of absolute maxima and minimum value does not exist.

Find the maximum or minimum value, if any, without using derivatives, of the function: –(x – 3)2 + 9

Answer»

It is given that f (x) = – (x – 3)² + 9

Here (x – 3)² ≥ 0

We can write it as

– (x – 3)² ≤ 0

By adding 9 on both sides

– (x – 3)² + 9 ≤ 0 + 9

Where f (x) ≤ 9

So the maximum value of f (x) = 9 which occurs at x = 3 which is the point of absolute maxima and minimum value does not exist.