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NDA2024MathematicsApplication of DerivativesActual

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

Options

  1. A- (1+ 2 )
  2. B- ( 1 2 + 2 )
  3. C- (1+ 4 )
  4. D-2 ( 1 2 - 4 )

Correct answer

A. - (1+ 2 )

Step-by-step solution

f(x)= 2 x+x on [- 2 , 2 ] Find the value of f(x) at boundary of interval i.e at x = - 2 and x = 2 aligned & f ( - 2 )=-1+ - 2 & f ( 2 )=-1+ 2 aligned So, minimum value of f ( x )^2=- (1+ 2 )

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