Calculus Homework

Name: __________________________________________________________ You must show all your work clearly.

1. Use Implicit differentiation to find Find the slope of the curve at the given point.

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2. Find the tangent line to the curve,

3. Two Planes approach an air traffic control tower. One flying due east at 340 mi/hr and the other flying due south at 280 mi/hr. Assuming that they fly at the same constant elevation, how fast is the distance between planes changing when east bound plane is at 400 miles from the tower and the south bound is 300 miles from the tower?

4. Find the Vertical Asymptotes and then determine the left and right limits at each vertical

asymptote. Find the limit if exists.

5. Find the Horizontal Asymptotes. If the function has no horizontal asymptote then, identify the end behavior of both ends.

6. Find the critical point( s) and the intervals on which the given function is increasing and decreasing. . = x3 + 5x – 1

7. Determine the intervals on which the given function is concave up or down. Identify the inflection points. = x4 - 24x2 + 1

8. Find the local extrema of

9. Find the absolute extrema of on [-2, 5].

10. Sketch the graph of . Identify symmetry, Increasing and decreasing intervals, local extrema, concavity, infection points, asymptotes, and x & y intercepts if they exist. You must show all your work to earn full credit. (20 Points).

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