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.
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
