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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

Put the value of x of all the options in f(x) and find value of f(x).
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why not a??
Because 1 is max value, not -1.

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

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 ...

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

## at x = 0,  f(x) = 1

edited
Nice ans using graph.Thanks :)