Find the intervals in which the function
$f(x) = 6 - 9x - x^2$
is strictly increasing or strictly decreasing.

Q: Find the intervals in which the function $f(x) = 6 - 9x - x^2$ is strictly increasing or strictly decreasing.

Explanation: We have: \[f'(x) = -9 - 2x\] Setting $f'(x) = 0$: \[x = -\dfrac{9}{2}\] In $\left(-\infty, -\dfrac{9}{2}\right)$, $f'(x) > 0$ ⟹ strictly increasing \[\] In $\left(-\dfrac{9}{2}, \infty\right)$, $f'(x) < 0$ ⟹ strictly decreasing

Question

Accepted Answer

Explanation: We have:
$$f'(x) = -9 - 2x$$

Setting $f'(x) = 0$:
$$x = -\dfrac{9}{2}$$

In $\left(-\infty, -\dfrac{9}{2}\right)$, $f'(x) > 0$ ⟹ strictly increasing

In $\left(-\dfrac{9}{2}, \infty\right)$, $f'(x) < 0$ ⟹ strictly decreasing

QPaperGen

Question:

Solution