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NDA2022MathematicsApplication of DerivativesActual

Where does the function f(x)= _ j=1 ^7(x-j)^2 attain its minimum value ?

Options

  1. Ax=3.5
  2. Bx=4
  3. Cx=4.5
  4. Dx=4

Correct answer

B. x=4

Step-by-step solution

aligned & f(x)= _ j=1 ^7(x-j)^2= _ j=1 ^7 (x^2-2 x j+j^2 ) & x^2 _ j=1 ^7 1-2 x _ j=1 ^7 j+ _ j=1 ^7 j^2 & =7 x^2-2 x 7(7+1) 2 + 7(7+1)(14+1) 6 & =7 x^2-56 x+140 & f^ (x)=14 x-56=0 x=4 & f^ (x)=14 0 aligned f(x) is minimum at x=4 .

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