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If f(x)= kx^3 + 9x^2 + 9x + 3 is increasing in each interval. Then find the value of k?

Asked by dasratna_72 21st May 2017, 8:35 PM
Answered by Expert
Answer:
begin mathsize 16px style As space function space is space increasing space then space
straight f apostrophe left parenthesis straight x right parenthesis greater than 0
3 kx squared minus 18 kx plus 9 greater than 0
kx squared minus 6 straight k plus 3 greater than 0
straight k greater than 0 space and space 36 straight k squared minus 12 straight k less than 0
straight k greater than 0 space and space straight k left parenthesis 3 straight k minus 1 right parenthesis less than 0
3 straight k minus 1 less than 0
straight k less than 1 third
straight f left parenthesis straight x right parenthesis space is space increasing space on space straight R space if space straight k element of open parentheses 0 comma 1 third close parentheses

end style
Answered by Expert 22nd May 2017, 9:41 AM
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