Question

Find the interval in which function f given by f(x) =
2 + 2 − 5 is
(1)strictly increasing (2)strictly decreasing .Find the interval in which function f given by f(x) =
2 + 2 − 5 is
(1)strictly increasing (2)strictly decreasing .

Answer 1

Answer:

f(x)=x

2

+2x−5

f

′

(x)=2x+2=2(x+1)

Put f

′

(x)=0

⇒x+1=0

⇒x=−1

Point x=−1 divide the real line in to 2 disjoint intervals.

(−∞,−1) and (−1,∞)

∴ when the value of x<−1 then x∈(−∞,−1) and f is strictly decreasing.

And when the value of x>−1 then x∈(−1,∞) and f is strictly increasing.

∴f is strictly decreasing in (−∞,−1) and is strictly increasing in (−1,∞)

Answer 2

Go through the attachment..