Find the intervals in which f (x) = –x^{2} – 2x + 15 is increasing or decreasing

### Asked by Topperlearning User | 6th Aug, 2014, 09:20: AM

** **we have,

*f* (*x*) = –*x*^{2} – 2*x* + 15

Þ *f (x*) = –2*x* – 2 = –2(*x* + 1)

For *f* (*x*) be increasing, we must have

*f *¢ (*x*) > 0

Þ –2(*x* + 1) > 0

Þ *x* + 1 < 0 [_{} – 2 < 0 and *ab* > 0, *a* < 0 Þ *b* < 0]

Þ *x* < – 1 Þ *x* Î (–¥, –1)

Thus, *f* (*x*) is increasing on the interval (–¥, –1)

For *f* (*x*) to be decreasing, we must have

*f*¢ (*x*) < 0

Þ –2(*x* + 1) < 0

Þ *x* + 1 > 0 [_{} – 2 < 0 and *ab* < 0, *a* < 0 Þ *b* > 0]

Þ *x* > –1 Þ *x* Î (–1, ¥)

So, *f* (*x*) is decreasing on (–1, ¥)

### Answered by | 6th Aug, 2014, 11:20: AM

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