Question

sketch the curve x=e^t, y=t^2e^t

A.) Find all points (x, y) at which the curve has a horizontal tangent
B.) Find the equation of the tangent at t = 1
C.) Write the equation in Cartesian (x-y) form.

Answer 1

ideally, I think youd rewrite it by solving t as a function of x; and using that to sub in the t spot in y

Answer 2

e^t = x ; so you can sub that whole mess there

but the other youd have to make explicit i think

Answer 3

so t=lnx and plug that into the y equation?