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NDA2024MathematicsApplication of DerivativesActual

Paragraph: Let f(x)= 2 x+x on [ - 2 , 2 ] Question: What is the greatest value of f(x) ?

Options

  1. A3 2 - 12
  2. B3 2 + 12
  3. C3 2 + 9
  4. D3 2 + 6

Correct answer

B. 3 2 + 12

Step-by-step solution

f(x)= 2 x+x on [- 2 , 2 ]f(x)=-2 2 x+1 for maxima & minima f(x)=0 aligned & 2 x= 1 2 & x= 12 or 5 12 ( Not in interval) of [ - 2 , 2 ] . aligned So, maximum value of f(x) occurs at x= 12 ie f ( 12 )= 6 + 12 = 3 2 + 12

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