can someone help me with this? he didn't lecture on finding points other than when t=0, so i am very, very lost. thanks. don't know where to start.

(1 pt) Use a graph to estimate the coordinates of the highest point and the leftmost point on the curve
x=4te^t,y=4te^−t.
Then find the exact coordinates.
Highest point: .
Leftmost point: .
The curve has one horizontal asymptote and one vertical asymptote. Find them.
Horizontal asymptote: y= .
Vertical asymptote: x= .

Question

can someone help me with this?  he didn't lecture on finding points other than when t=0, so i am very, very lost.  thanks.  don't know where to start.

(1 pt) Use a graph to estimate the coordinates of the highest point and the leftmost point on the curve
x=4te^t,y=4te^−t.
Then find the exact coordinates. 
Highest point:   . 
Leftmost point:  . 
The curve has one horizontal asymptote and one vertical asymptote. Find them. 
Horizontal asymptote: y=  . 
Vertical asymptote: x=  .

anonymous · Answer

@amistre64 , you've helped before.  can you help me now?

anonymous · Answer

ok, well, i have to go to bed.  i'll check back later and hopefully someone will have answered me by then...

amistre64 · Answer

im thinking like this:

the leftmost point is when x stops moving and turns back around

x = 4t e^t

x' = 4 e^t + 4t e^t 
   = 4e^t (1+t)

since 4e^t is always positive .... 

at t = -1 the slope is 0
at t < -1, the slope is negative
at t > -1 the slope is positive

|dw:1384900957140:dw|