Application of Derivatives — MATHS STD 12 Science — Question
Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSApplication of Derivatives1 Mark
Question
Find the interval in function $6 - 9x - x^2$ is increasing or decreasing.
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Answer
It is given that function $f(x) = 6 - 9x - x^2$
$f'(x) = -9 - 2x$
If $f'(x) = 0,$
$\Rightarrow x=\frac{-9}{2}$
So, the point $x = \frac{-9}{2}$ divides the real line two disjoint intervals, $\left(-\infty, \frac{-9}{2}\right)$ and $\left(\frac{-9}{2}, \infty\right)$
So, in interval $\left(-\infty, \frac{-9}{2}\right)$
$f'(x) = -9 - 2x > 0$
Therefore, the given function '$f\ '$ is strictly increasing for $x < \frac{-9}{2}$.
And in interval $\left(\frac{-9}{2}, \infty\right)$
$f'(x) = -9 - 2x < 0$
Therefore, the given function $'f\ '$ is strictly decreasing for $x>\frac{-9}{2}$
Thus, f is strictly decreasing for $x>\frac{-9}{2}$
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