Trig max/min problems: straight-line segments are drawn....

[chengeto]

Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, with coordinates (x,0)on the positive x-axis. Assuming that 0 ? x ? 3, the angle ? between the two line segments PP1 and PP2 is given by the relation ?= ?-arccotx-arccot(3-x/2). Determine the value of x which makes ? as large as possible.

My attempt to solution:

Max value of theta occurs when x=0


?= ?-arccotx-arccot(3-x/2)

?= ?-arccot(0)-arccot(3-0/2)

I don't know if l am on the right path for this question

 

[Deleted member 4993]

Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, with coordinates (x,0)on the positive x-axis. Assuming that 0 ? x ? 3, the angle ? between the two line segments PP1 and PP2 is given by the relation ?= ?-arccotx-arccot(3-x/2). Determine the value of x which makes ? as large as possible.

My attempt to solution:

Max value of theta occurs when x=0


?= ?-arccotx-arccot(3-x/2)

?= ?-arccot(0)-arccot(3-0/2)

I don't know if l am on the right path for this question

Is x = 0[sup:2smhn0rb]-[/sup:2smhn0rb] a possible situation?

If it is then you are in the right direction - be careful choosing value for arccot(0[sup:2smhn0rb]-[/sup:2smhn0rb])

 

[chengeto]

Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, with coordinates (x,0)on the positive x-axis. Assuming that 0 ? x ? 3, the angle ? between the two line segments PP1 and PP2 is given by the relation ?= ?-arccotx-arccot(3-x/2). Determine the value of x which makes ? as large as possible.

My attempt to solution:

Max value of theta occurs when x=0


?= ?-arccotx-arccot(3-x/2)

?= ?-arccot(0)-arccot(3-0/2)

I don't know if l am on the right path for this question

Is x = 0[sup:nfgwrr7r]-[/sup:nfgwrr7r] a possible situation?

If it is then you are in the right direction - be careful choosing value for arccot(0[sup:nfgwrr7r]-[/sup:nfgwrr7r])

I found my mistake. I am supposed to find first \(\displaystyle \frac{d\theta}{dx}\) and then find the critical points of the relation l am given. Let me try that and if l am stuck l will come back