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Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are:

 

  1. 0, -1
  2. -1, 0
  3. 0, 1
  4. -1, 2
asked in Set Theory & Algebra by Veteran (99k points) | 725 views
Answer could be obtained via graph plotting techanique.

4 Answers

+12 votes
Best answer
Answer: C

Put the value of x of all the options in f(x) and find value of f(x).
answered by Veteran (35.6k points)
selected by
why not a??
Because 1 is max value, not -1.
Please elaborate the answer

two values are given in each option.which one to put and which one not to put.

please explain step by step
the question asks "at what x the function has a maximum value" (answer is 0) and "what is that maximum value" (answer is 1)
what is wrong with this approach ?

f'(x) = 0 and so am not getting any stationary points

So am computing end points f(1) = 0 and f(-1) = 0 and so option is B)

I understand that we are getting maximum value at x=0 but why maxima/minima concept is showing different answer ? please clear this ...
+4 votes

there are 2 parts 

part A says "value of x at which the function attains a maximum" so at x=0 ,function attains a maximum and

part B says "the maximum value of the function"  so f(0)=1-0=1

so ans should be 0,1

answered by Loyal (3.5k points)
+3 votes

 

here in diagram clear see that,

at x=0 f(x) would be maximum which is 1

or

at x = 0,  f(x) = 1

answered by (283 points)
edited by
Nice ans using graph.Thanks :)
+1 vote
There is three values of x = -1,0,1

1-|x| =1-|-1| = 0

1-|x| = 1- |0|=1

1-|x| = 1-|1| =0

so option C 0,1
answered by Boss (7.3k points)


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