The maximum and the minimum values, if any of the following functions f (x) = –| x – 1 | + 5 for all

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

We have

f (x) = –|x – 1| + 5 for all
Now,
 for all
  for all
  for all
f (x)  5 for all
So, 5 is the maximum value of f (x)
Now,
f (x) = 5  – |x –1|+ 5 = 5 |x – 1|
= 0  x = 1
Thus f (x) attains the maximum value 5 at
x = 1
Since f (x) can be made as small as we please therefore the minimum value of f (x) does not exist

Answered by  | 4th Jun, 2014, 03:23: PM