Question Number 114753 by bemath last updated on 21/Sep/20

find minimum value of function  f(x) = (((x+17)^3 )/x) , 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

Commented bybemath last updated on 21/Sep/20

give thanks