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Question Number 114753 by bemath last updated on 21/Sep/20
find minimum value of function  f(x) = (((x+17)^3 )/x) , x>0
findminimumvalueoffunctionf(x)=(x+17)3x,x>0
Answered by Olaf last updated on 21/Sep/20
f′(x) = ((3(x+17)^2 x−(x+17)^3 )/x^2 )  f′(x) = (((x+17)^2 (3x−(x+17)))/x^2 )  f′(x) = (((x+17)^2 (2x−17))/x^2 )  f′(x) = 0 ⇔ x = ((17)/2) (x > 0)  If x < ((17)/2), f′(x) < 0  If x > ((17)/2), f′(x) > 0  ⇒ x = ((17)/2) is a minimum
f(x)=3(x+17)2x(x+17)3x2f(x)=(x+17)2(3x(x+17))x2f(x)=(x+17)2(2x17)x2f(x)=0x=172(x>0)Ifx<172,f(x)<0Ifx>172,f(x)>0x=172isaminimum
Commented by bemath last updated on 21/Sep/20
give thanks
givethanks

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