GATE CSE 2015 Set 2 | Question: GA-3

Question

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:

• A. $0, -1$
• B. $-1, 0$
• C. $0, 1$
• D. $-1, 2$

Comments

Answer could be obtained via graph plotting techanique.

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if you think why option A is not a correct answer then my friend you didn’t read the question well enough.

In the question it says → The value of x at which the function attains a maximum(in this case our answer is at point 0), and the maximum value of the function are(maximum value of the function in the given range (-1 to 1) on point x=0 is 1) 

so the answer is option C(The question didn’t asked if function achieved the highest value at point zero and lowest on point -1)

Answer 1

 

Here in diagram we can clearly see that,
At $x=0,$ $f(x)$ would be maximum which is $1.$

Option C is correct.
 

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Alternate Approach - 
Put the value of $x$ of all the options in $f(x)$ and find the value of $f(x).$

Comments

Nice ans using graph.Thanks :)

Answer 2

Answer: C

Put the value of x of all the options in f(x) and find value of f(x).

Comments

why not a??

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Because 1 is max value, not -1.

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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

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the question asks "at what x the function has a maximum value" (answer is 0) and "what is that maximum value" (answer is 1)

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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 ...

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But if we check option B and we substitute -1 inside the modulus then ultimately the result is +ve and what we get is

1 - |-1| =>1-1=0 and the option was (-1,0) so in this scenario both options B and C appear to be correct please tell me the logic behind using modulus here because i am really confused.

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@  , I too have similar confusion.

Focus on the wordings of the question.

• The value of x at which the function attains a maximum, and
• the maximum value of the function are

See the final graph given in the best answer.

Now ask question to yourself..

• On which value of “x”, function attains the maximum value. → on x = 0.
• After putting all the values of “x”(Say -1, 0, 1), what is the maximum value of the function. → maximum value of function = 1, which is at value x = 0.

Hence answer = 0, 1.

 

What a question! Simple but higher chances of silly mistake.

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@Vicky rix same doubt , if you get answer of your query then please explain to me.

Answer 3

There are three values of $x = -1,0,1$

$\Rightarrow 1-|x| =1-|-1| = 0$
$\Rightarrow1-|x| = 1- |0|=1$
$\Rightarrow 1-|x| = 1-|1| =0$

so option C 0,1

Answer 4

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