Question

Find the interval in which function f given by f(x) =x²+2x− 5 is
(1)strictly increasing (2)strictly decreasing .

Answer 1

Answer:

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

(−∞,−1) and (−1,∞)

Step-by-step explanation:

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

Answer:

Refer the attachement for better understanding

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