Max/Min Question (1 Viewer)

[kelly_xxx]

A point A lies on the curve y= x(5-x), and a point B with the same x coordinate as A lies on the curve y=x(x-3). Show this information on a diagram , then find an expression for the length of AB, and determine the max. length if 0<x<4 (this is meant to be smaller equal than)

Would u be able to show me the working? Much appreciated.

 

[Riviet]

Let co-ordinates of A be (x,y₁) and B be (x,y₂)
Use distance formula:
d=sqrt[(y₂-y₁)²-(x-x)]
=sqrt(y₂-y₁)²
=|y₂-y₁|

Please clarify what you mean by 0<4.

 

[Sober]

A point A lies on the curve y= x(5-x), and a point B with the same x coordinate as A lies on the curve y=x(x-3). Show this information on a diagram , then find an expression for the length of AB, and determine the max. length if 0<x<4 (this is meant to be smaller equal than)

Would u be able to show me the working? Much appreciated.

The distance will be the absolute difference of the two y values as Riviet stated:

AB = | x(5-x) - x(x-3) |

= | 2x² - 8x |

And I assume you were looking for the maximum for 0 ≤x ≤ 4, so for a porabola this is going to be either the turning point (if it is in the range), or the defined end points at 0 and 4:

Turning point = 2, 8
End points = (0,0), (4,0);

The turning point is in the range and is greater than the end points so the answer is 8.