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MHT CET202415 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If f (x)=x^3-10 x^2+200 x-10 , then

Options

  1. Af (x) is decreasing in (- , 10] and increasing in [10, )
  2. Bf (x) is increasing in (- , 10] and decreasing in [10, )
  3. Cf (x) is increasing throughout real line
  4. Df (x) is decreasing throughout real line

Correct answer

C. f (x) is increasing throughout real line

Step-by-step solution

aligned & f (x)=x^3-10 x^2+200 x-10 & f ^ (x)=3 x^2-20 x+200 aligned For f (x) to be increasing f ^ (x) 0 aligned & 3 x^2-20 x+200 0 & 3 (x^2- 20 3 x+ 200 3 + 100 9 - 100 9 ) 0 & 3 [ (x- 10 3 )^2+ 500 9 ] 0 & 3 (x- 10 3 )^2+ 500 3 0 aligned Always increasing throughout real line.

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