32 votes 32 votes 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: $0, -1$ $-1, 0$ $0, 1$ $-1, 2$ Calculus gatecse-2015-set2 set-theory&algebra functions normal maxima-minima + – go_editor asked Feb 12, 2015 go_editor 6.8k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Chhotu commented Sep 29, 2017 reply Follow Share Answer could be obtained via graph plotting techanique. 0 votes 0 votes kickassakash commented Jul 15, 2023 reply Follow Share 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) 0 votes 0 votes Please log in or register to add a comment.
Best answer 31 votes 31 votes Here in diagram we can clearly see that, At $x=0,$ $f(x)$ would be maximum which is $1.$ Option C is correct. Alternate Approach - Put the value of $x$ of all the options in $f(x)$ and find the value of $f(x).$ ram_18051996 answered Aug 1, 2017 • edited Jan 12, 2023 by shadymademe ram_18051996 comment Share Follow See 1 comment See all 1 1 comment reply Warrior commented Aug 12, 2017 reply Follow Share Nice ans using graph.Thanks :) 1 votes 1 votes Please log in or register to add a comment.
17 votes 17 votes Answer: C Put the value of x of all the options in f(x) and find value of f(x). Rajarshi Sarkar answered Feb 12, 2015 Rajarshi Sarkar comment Share Follow See all 8 Comments See all 8 8 Comments reply Show 5 previous comments tanishk1999 commented Apr 9, 2020 reply Follow Share 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. 0 votes 0 votes nocturnal123 commented Oct 6, 2020 i edited by nocturnal123 Oct 6, 2020 reply Follow Share @ , 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. 0 votes 0 votes Shaikh727 commented Sep 22, 2022 reply Follow Share @Vicky rix same doubt , if you get answer of your query then please explain to me. 0 votes 0 votes Please log in or register to add a comment.
12 votes 12 votes 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 Rishi yadav answered Oct 12, 2017 • edited Jan 26, 2020 by Rishi yadav Rishi yadav comment Share Follow See all 0 reply Please log in or register to add a comment.
7 votes 7 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 Anil Khatri answered Jan 4, 2017 Anil Khatri comment Share Follow See all 0 reply Please log in or register to add a comment.