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The function f (x) is given by f(x) = 2/sqrt(x) + px , where p is a real constant and x > 0 . Given that f '(2) = 5 , find p , giving your answer in the form a +b sqrt(2) , where a and b are rational numbers.

 Dec 3, 2018
 #1
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f(x) = 2x^(-1/2) +px

 

f'(x) = -x^(-3/2) + p

 

f '(2) = 5       means that

 

- (2)^(-3/2) + p = 5

 

-1 / √8 + p = 5

 

p = [ 5 + 1/√8 ] =

 

[ 5 + 1 / [ 2√2] ]  =

 

[ 5 + √2 / 4]  = 

 

5 + (1/4)√2

 

 

cool cool cool

 Dec 3, 2018

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