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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=1-x^3-x^5$ is decreasing for
  • A
    $1 \leq x \leq 5$
  • B
    $x \leq 1$
  • C
    $x \geq 1$
  • ✓
    all values of $x$
✓

Answer

Correct option: D.
all values of $x$
(d) : Given, $f(x)=1-x^3-x^5$
Differentiating w.r.t. $x$, we get
$
f^{\prime}(x)=-3 x^2-5 x^4
$
$\Rightarrow f^{\prime}(x)=-\left(3 x^2+5 x^4\right) \Rightarrow f^{\prime}(x)<0$ for all values of $x$.

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