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# Why can a gradient be infinity ? watch

question 5 b you need to make the gradient 0 which i understand as thats the maximum point of the circle however the mark scheme says that you must also make dy/dx equal to infinity which i do not understand how on earth could a gradient be forever big and small?
those are the solutions.
2. (Original post by BubbleBabby)
question 5 b you need to make the gradient 0 which i understand as thats the maximum point of the circle however the mark scheme says that you must also make dy/dx equal to infinity which i do not understand how on earth could a gradient be forever big and small?
those are the solutions.
Infinite gradient is just used to denote the gradient of vertical line. It doesnt really make sense to make it equal infinity as infinity is not a number, but writing dy/dx=infinity gets the notion of infinite steepness across.

The alternative notation would be to say that dx/dy=0
3. The gradient (dy/dx) is meant as change in y/change in x.

In a vertical line, the change in y is infinity (it rises from -infinity to infinity) and the change in x is 0 hence the gradient = infinity. But it's not an number.

Hence dy/dx = infinity but this isn't useful --> take reciprocals of both sides: 1/dy/dx = 1/infinity --> dx/dy = 0.

In a horizontal line, the change in y is 0 but change in x is infinity therefore the gradient is 0 and dy/dx = 0 but dx/dy = infinity.
4. (Original post by RDKGames)
Infinite gradient is just used to denote the gradient of vertical line. It doesnt really make sense to make it equal infinity as infinity is not a number, but writing dy/dx=infinity gets the notion of infinite steepness across.

The alternative notation would be to say that dx/dy=0
ooooooooh ok because it's infanitly steep! i get it!!!! Thank you!!!

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