Find the intervals in which the function
$f(x) = 10 - 6x - 2x^2$
is strictly increasing or strictly decreasing.

Q: Find the intervals in which the function $f(x) = 10 - 6x - 2x^2$ is strictly increasing or strictly decreasing.

Explanation: We have: \[f'(x) = -6 - 4x\] Setting $f'(x) = 0$: \[-6 - 4x = 0 \Rightarrow x = -\dfrac{3}{2}\] In $\left(-\infty, -\dfrac{3}{2}\right)$, $f'(x) > 0$ ⟹ strictly increasing \[\] In $\left(-\dfrac{3}{2}, \infty\right)$, $f'(x) < 0$ ⟹ strictly decreasing

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Accepted Answer

Explanation: We have:
$$f'(x) = -6 - 4x$$

Setting $f'(x) = 0$:
$$-6 - 4x = 0 \Rightarrow x = -\dfrac{3}{2}$$

In $\left(-\infty, -\dfrac{3}{2}\right)$, $f'(x) > 0$ ⟹ strictly increasing

In $\left(-\dfrac{3}{2}, \infty\right)$, $f'(x) < 0$ ⟹ strictly decreasing

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