# Find the interval in which f(x) = $$-x^2 – 2x + 15$$ is increasing or decreasing.

## Solution :

We have,  f(x) = $$-x^2 – 2x + 15$$

$$\implies$$ f'(x) = -2x – 2 = -2(x + 1)

for f(x) to be increasing, we must have

f'(x) > 0

-2(x + 1) > 0

$$\implies$$ x + 1 < 0

$$\implies$$ x < -1 $$\implies$$ x $$\in$$ $$(-\infty, -1)$$.

Thus f(x) is increasing on the interval $$(-\infty, -1)$$.

for f(x) to be decreasing, we must have

f'(x) > 0

-2(x + 1) < 0

$$\implies$$ x + 1 > 0

$$\implies$$ x > -1 $$\implies$$ x $$\in$$ $$(-1, \infty)$$.

Thus f(x) is decreasing on the interval $$(-1, \infty)$$.

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