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Calculus I.S.I. and C.M.I. Entrance ISI Entrance Videos

Derivative of Function Problem | TOMATO BStat Objective 756

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on a derivative of Function. You may use sequential hints to solve the problem.

Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Derivative of Function.

Derivative of Function Problem (B.Stat Objective Question )


Let f(x)=x[x] where [x] denotes the greatest integer smaller than or equal to x where x is not an integer, what is f'(x)?

  • 2x
  • [x]
  • 2[x]
  • it does not exist.

Key Concepts


Equation

Derivative

Algebra

Check the Answer


But try the problem first…

Answer: [x].

Source
Suggested Reading

B.Stat Objective Problem 756

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

\(f(x)=x[x]\) where f(x) discontinuous at integer points so non differentiable at those pts

so we find for non-integer points

Second Hint

if x is not an integer then [x] is a constant and not equal to x

Final Step

x is non integer so here [x] is treated as constant here . Let [x] = a then f(x) =ax => f'(x)= a = [x] . Hence option [x] is correct.

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