Find the intervals in which the following function are strictly i… - Vidyadip

Question

Find the intervals in which the following function are strictly increasing or decreasing:
$6 - 9x - x^2$

✓

Answer

Given: $\text{f}\text{(x)} = 6-9\text{x} - \text{x}^2\ \Rightarrow\ \text{f}'\text{(x)} = -9 - 2\text{x}$
$\text{Now }-9-2\text{x} = 0\ \Rightarrow\ \text{x}=\frac{-9}{2}$
Therefore, we have three disjoint intervals $ \bigg(-\infty,\ \frac{-9}{2}\bigg)\text {and}\bigg(\frac{-9}{2},\ \infty\bigg).$
For interval $\bigg(-\infty,\ \frac{-9} {2}\bigg),\ \text{x}<\frac{-9}{2}$
Therefore, f is strictly increasing.
For interval $\bigg (\frac{-9}{2},\ \infty\bigg),\ \text{x}>\frac{-9}{2}$
Therefore, f is strictly decreasing.

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