Find the intervals in which f (x) = –x2 – 2x + 15 is increasing or decreasing

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

Expert Answer:

 we have,

f (x) = –x2 – 2x + 15

Þ f (x) = –2x – 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