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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