Question

Please answer the following with detailed explainations.

1). Find the slopes of the tangent lines to the given curves at the indicated points.

x= t^3 - t, y=t^4 - 5t^2 + 4, a) t= -1, b) t= 1, c) (0,4)

2) Find the slopes of the tangent lines to the given curves at the indicated points.

x= cos 2t, y= sin 3t, a) t= pi/2, b) t= 3pi/2, c) (1,0)

3) Sketch the graph and find the slope of the curve at the given point.

x=t^3 - t, y= t^4 - 5t^2 + 4, at (0,0)

4) Identify all points at which the cuve has a) horizontal tangent and b) a vertical tangent.

x= cos 2t, y =sin 7t

5) Find the area enclosed by the given curve.

x= tsin t, y= tcos t, from -pi/2 <= t <= pi/2

Thank you!