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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
Let $f$ and $g$ be increasing and decreasing functions, respectively from $[0 , \infty )$ to $[0 , \infty )$. Let $h (x) = f [g (x)]$ . If $h (0) = 0$, then $ h (x) - h (1)$ is
  • ✓
    always zero
  • B
    strictly increasing
  • C
    always negative
  • D
    always positive
✓

Answer

Correct option: A.
always zero
a
$x \geqslant y \geqslant 0$

$g(y) \geqslant g(x)$

$f(g(y)) \geqslant f(g(x)) \quad \forall x \in[0, \infty)$

$h(y) \geqslant h(x) \quad \forall \quad x \geqslant y$

$h(x)$ is a decressing $f^{n} \quad \forall x \in[0, \infty)$

$\forall \quad x  \geqslant 0$

$k_{t}(0) \geqslant  h(x)$

$n(x) \leq 0 \quad \forall x \geqslant 0$

$h(x) \geqslant 0 \quad \forall \quad x \geqslant 0$

$h(x)=0$

$h(x)-h(1)$

$0-0$

$=0$

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