Consider an object moving along the parametrized curve with equations: x(t)=e² + e², y(t)=-* where t is in the time interval [0,1] seconds. Recall that the speed of a parametric curve is given by s(t) = √(x'(t))² + (y'(t))². (a) The maximum speed of the object on the time interval is at time (b) The minimum speed of the object on the time interval is at time

Find an equation, in slope-intercept form, of the line tangent to the curve with parametric equations x = t²+2t and y = 2 lnt at the point (3,0). y =

Consider the parametric equations y = e' +t te [1, 10] Briefly explain how you know that the curve is only traversed one time fromt = 1 to t = 10.

Find the curve y if dy = x2 +5, dx +5, curve passes through (0, 25)***

A spaceship travels on a path given by p(t) = (t, t^2 - 2t, t^2).(a) Find an equation for the tangent line to the path of the particle at t = 3.(b) The crew of the spaceship is tasked with the job of deflecting an asteroid in orderto save planet Earth. The spaceship is equipped with a laser beam that can firestraight ahead. The asteroid is located at (5,11, 21). At what time should the crewfire the laser?

Find the slope of the curve whose parametric equation is given by y = t³ + t²+ 1/t and x = t⁴ + 3t² when t = 1/2.

Calculate y” and y”’