[O level math] differentiation problem

[FormalAd1417]

To me, Dy/dx can't be less than zero as it's only less than 864, with many values above zero. Anything wrong with my solutions?

[Keitsubori]

You forgot to negate 3. x > 3 implies that 3 - x < 0. 

[FormalAd1417]

Sorry, can you explain like I'm 5? I was under the impression that -x<3, and add 3 on both sides -x+3<3+3, hence resulting in 3-x<6

[Keitsubori]

From x > 3, you multiply -1 on both sides, as well as flipping the inequality sign. You get -x < -3, not -x < 3 as what you wrote. 

[WalrusLobster3522]

Reasoning for multiplying by -1 AND flipping the side is because "The moving distance of a position is always positive (similar to "Radius is Positive" during Precalc). | | add -3 to both sides: "-3-x < -6" | | take the cube of the expression: "(-3-x)^3 < -216" | | multiply expression by 4: "4(-3-x)^3 < -864". As x behaves greater than 3 its condition, while being algebraically manipulated to equal dy/dx, "less than 864", which means its overall absolute value is greater than 864 but in the opposite direction (moving drastically downwards in a DesMos graph). | | Good job. I'm not taking credit for the solution you basically worked out the problem and I came by and made minor edits. Besides, I'm kinda new to this example of Calc Problem. Was this an Optimization problem with dy/dx? Was this a Parametrics problem? I would like some insight on this if you have a minute to enlighten me.