2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Applications of Derivatives

JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Maxima and Minima

  • question_answer
    If \[x+y=16\] and \[{{x}^{2}}+{{y}^{2}}\] is minimum, then the values of x and y are

    A)            3, 13

    B)            4, 12

    C)            6, 10

    D)            8, 8

    Correct Answer: D

    Solution :

               \[x+y=16\Rightarrow y=16-x\]Þ \[{{x}^{2}}+{{y}^{2}}={{x}^{2}}+{{(16-x)}^{2}}\]                    Let \[z={{x}^{2}}+{{(16-x)}^{2}}\Rightarrow z'=4x-32\]                    To be minimum of \[z,\,\,z''>0\], and it is.                    Therefore \[4x-32=0\Rightarrow x=8\Rightarrow y=8\]


You need to login to perform this action.
You will be redirected in 3 sec spinner