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Application Of Derivatives

Question
CBSEENMA12035302
Wired Faculty App

Find the intervals in which the following functions are strictly increasing or decreasing:
10 – 6x – 2x2

Solution

Let  straight f left parenthesis straight x right parenthesis space equals space 10 minus 6 straight x minus 2 straight x squared space                             therefore space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space minus 6 minus 4 straight x
Now,  straight f apostrophe left parenthesis straight x right parenthesis greater than 0 space space space space space when space space space minus 6 minus 4 straight x space greater than 0 space space space space space straight i. straight e. space when space straight x space less than negative 3 over 2.
therefore space space space space space straight f left parenthesis straight x right parenthesis space is space increasing space in space open parentheses negative infinity comma space minus 3 over 2 close parentheses.
  Also space straight f apostrophe left parenthesis straight x right parenthesis space less than space 0 space space space when space minus 6 minus 4 straight x space less than 0 space space space straight i. straight e. space when space straight x space greater than space minus 3 over 2. therefore space space space space straight f left parenthesis straight x right parenthesis space is space decreasing space in space open parentheses negative 3 over 2 comma space infinity close parentheses.

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