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  4. The function f(x) = 1 - x3 - x5 is decreasing for

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Q. The function $f(x) = 1 - x^3 - x^5$ is decreasing for

Application of Derivatives

Solution:

Given that, $f(x) = 1 - x^3 - x^5$
On differentiating w.r.t. $x$, we get
$f(x) = - 3x^2 - 5x^4$
$\Rightarrow f\left(x\right) = - \left(3x^{2} + 5x^{4}\right)$
$\Rightarrow f\left(x\right) < 0$ for all values of $x$.