Rates of change question (1 Viewer)

[pikachu975]

i) y = 8x - x^2
Find rate of change of x coordinate when rate of change of y coordinate is 20.
I got 5/3 for this.

The one I need help with:
ii) Find the coordinates of the point on the curve where the x coordinate and y coordinate of P are increasing at the same rate.

Oh sorry the first part is the rate of change when x = -2, sorry for forgetting this.

 

[KingOfActing]

Low key might be having an aneurysm from not touching maths for so long but is the question missing any information?

For the first part:

 

[InteGrand]

i) y = 8x - x^2
Find rate of change of x coordinate when rate of change of y coordinate is 20.
I got 5/3 for this.

The one I need help with:
ii) Find the coordinates of the point on the curve where the x coordinate and y coordinate of P are increasing at the same rate.

Hint for part (ii): if dy/dt = dx/dt on the curve, we are looking for where dy/dx = 1.

(In principle, a point where dx/dt and dy/dt are both zero would do, but we'd need to be given x(t) explicitly for that. (And note dy/dt = (dy/dx)*(dx/dt) = (8 – 2x(t))*(dx/dt), so dy/dt is automatically zero if dx/dt is zero at some time point.))

 

[pikachu975]

Edited the first part with info I forgot