GATE CSE 2015 | Set 2 | GA | Question: 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

@kickassakash exactly did the same mistake bro thanks for correcting me

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How will we know in exam that we have to plot the graph? @Chhotu

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Easiest question even seen. No need for graphs/putting all values. Simple 1-|x| is max when |x|=0.

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 :)

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Cant we find max, min values by making f'(x) = 0. here?. Is it because f(x) is not differenciable here?

Answer 2

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

Comments

best approach

Answer 3

Answer: C

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

Comments

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 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

Comments

Anyone here who got confused just because they thought - the points of maximum and minimum value :) 🙋🏻‍♀️

Answer 5

given f(x) = 1-|x|  on -1 <= x <= 1

f(x) can be written as :

f(x) = {1-(-(x))  if x<0

             or

           1-(x)   if x>=0}

now take x = -1 :

since x<0 : substitute value of x in 1-(-(x)) . 

1-(-(-1)) = 1-(1) = 0

for x = -1 value is 0 .

now take x = 0:

since x=0 : substitute value of x in 1-(x) . 

1-(0) = 1-(0) = 1

for x >= 0 value is 1 .

now take x = 1:

since x >= 0 : substitute value of x in 1-(x) . 

1-(1) = 1-(1) = 0

for x = 1 value is 0 .

we can observe for value x = 0 . we got maximum value of the function  which is 1 . 

so the answer is x =0 , 1  . 

option c .