1. Find dy/dx and d²y/dx².

x=t²+4, y=t²+7t

For which values oftis the curve concave upward? (Enter your answer using interval notation.)

2. Find dy/dxandd²y/dx².

x=e^t, y=te^t

For which values oftis the curve concave upward? (Enter your answer using interval notation.)

3. Show that the curve

x=5cos(t),y=4sin(t)cos(t) has two tangents at (0, 0) and find their equations.

y=

(smaller slope) y=

(larger slope) Sketch the curve.

4. Find the exact length of the curve.

x = 1 + 12t², y = 2 + 8t³, 0 t 4

5. Sketch the curve with the given polar equation by first sketching the graph of r as a function of in Cartesian coordinates.

r² = 9