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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
Let $h(x)=$ $\frac{{5{{(f(x))}^3}}}{3} + \frac{{{{(f(x))}^2}}}{2} + 2f(x)+ 100$ Where $f(x)$ is a differentiable function. Then which one of the following is correct
  • A
    $h(x)$ always increases
  • B
    $h(x)$ always decreases
  • ✓
    $h(x) $ increases as $f(x)$ increases
  • D
    $h(x)$ increases as $f(x) $ decreases
✓

Answer

Correct option: C.
$h(x) $ increases as $f(x)$ increases
c
$h^{\prime}(x)=\left(5(f(x))^{2}+f(x)+2\right) f^{\prime}(x)$

$h^{\prime}(x)=(f(x))(+v e)$

as $f(x)$ increases, $h(x)$ increases.

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