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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
$f(x)=x-[x]$ in the interval $[0,1]$ is
  • ✓
    increasing
  • B
    decreasing
  • C
    neither increasing nor decreasing
  • D
    none of these
✓

Answer

Correct option: A.
increasing
(a) : Given $f(x)=x-[x], x \in[0,1]$
But for $0 \leq x \leq 1,[x]=0, \therefore f(x)=x-0=x$ in $[0,1]$.
Let $x_1, x_2 \in[0,1]$ be such that $x_1$ < $x_2$ 
=> $f\left(x_1\right)$ < $f\left(x_2\right)$ => $f$ is increasing in $[0,1]$.

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