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Application Of Derivatives

Question
CBSEENMA12035301
Wired Faculty App

Find the intervals in which the following functions are strictly increasing or decreasing:
x2+ 2x – 5

Solution

Let straight f left parenthesis straight x right parenthesis space equals space straight x squared plus 2 straight x minus 5 space space space space space space space space space space space therefore space space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 2 straight x plus 2
Now,   straight f apostrophe left parenthesis straight x right parenthesis greater than 0 space space when space 2 straight x plus 2 greater than 0 space space space straight i. straight e. space space space when space straight x greater than negative 1
therefore space space space space straight f left parenthesis straight x right parenthesis space is space increasing space in space left parenthesis negative 1 comma space infinity right parenthesis.
Also,  straight f apostrophe left parenthesis straight x right parenthesis less than 0 space when space 2 straight x plus 2 less than 0 space space space space straight i. straight e. space when space straight x space less than space minus space 1
therefore space space space space straight f left parenthesis straight x right parenthesis space is space decreasing space in space left parenthesis negative infinity comma space minus 1 right parenthesis.

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