Cartesian Coordinates?

Question

What exactly are Cartesian Coordinates? I have a question, At what Cartesian Coordinates does the tangent line have slope equal to 5? This is referring to x=ln(t) and y=(t^2)/2+ln(t)

Answer 1

Cartesian coordinates use a vertical and horizontal axis, ( y-axis and x-axis, respectively), to show the relationship between y and x.

You are referring to a parametric equation between x and y where t is the parameter. You can get the the equation in the form of y = f(x) by elimimating t.

You can also just plot the function by computing values of x and y for various values of t. You can see that t>0 since ln(t ) is undefined for t =< 0.