Find the intervals in which the function
$f(x) = x^2 + 2x - 5$
is strictly increasing or strictly decreasing.

Q: Find the intervals in which the function $f(x) = x^2 + 2x - 5$ is strictly increasing or strictly decreasing.

Explanation: We have: \[f'(x) = 2x + 2\] Setting $f'(x) = 0$: \[2x + 2 = 0 \Rightarrow x = -1\] In $(-\infty, -1)$, \[f'(x) 0 ⟹ \text{strictly increasing}\]

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Accepted Answer

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

Setting $f'(x) = 0$:
$$2x + 2 = 0 \Rightarrow x = -1$$

In $(-\infty, -1)$, $$f'(x) < 0 ⟹ \text {strictly decreasing}$$

In $(-1, \infty)$, $$f'(x) > 0 ⟹ \text{strictly increasing}$$

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