What are the local maxiumum and minimum points for the function f(x)=(3x)/(2x^2-18)
+128475 As can be seen here : https://www.desmos.com/calculator/yhtjmyvehq
This function has no local max or min
+128475 I found the first derivative here : https://web2.0calc.com/questions/what-are-the-first-and-second-derivatives-of-the
as
-6 (x^2 + 9) (2x^2 - 18)^(-2) .........set this to 0
-6 (x^2 + 9)
__________ = 0 multiply each side by (2x^2 - 18) and we get
(2x^2 -18)^2
-6 (x^2 + 9) = 0 divide both sides by - 6
x^2 + 9 = 0
Note that the left side is > 0 for all x
Thus....there are no critical points ( max's or mins )
+128475 I could have taken the first derivative a little farther
-6 ( x^2 + 9) -6(x^2 + 9) -6 (x^2 + 9) -3 (x^2 + 9)
___________ = ____________ = ____________ = _________
(2x^2 - 18)^2 [ 2(x^2 - 9) ]^2 4 (x^2 - 9)^2 2 (x^2 - 9)
This is confirmed by WolframAlpha : https://www.wolframalpha.com/input/?i=derivative++(3x)+%2F+(2x%5E2+-+18)
Regardless.....there are still no max's or mins
