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Q.
In which of the following intervals, the function $ y(x) = x^3 - 3x^2 - 9x + 5 $ is always decreasing?
J & K CETJ & K CET 2017Application of Derivatives
Solution:
We have, $y (x) =x^{3}-3x^{2}-9x+5 \dots (i)$
Differentiating (i) w.r.t. x, we get
$y'(x)=3x^{2}-6x-9$
$=(x-3)(3x+3)$
Now, $y'(x)=0$
$\Rightarrow x=3$ and $-1$
Sign change for $y'{(x)}$
Hence, $y(x)$ is decreasing in $(-1, 3)$
