Question

1. What are the four basic shapes/combinations of first and second deriva tives? One common problem is forgetting to check where the first or second deriva tive does not exist. These are also critical/inflection points. Consider the x = t-sin(t y 1-cos(t) parametric function where-2π < t < 2T. 2. What are the first and second derivatives? 3. Where are the first and second derivatives equal to 0? 4. Where are the first and second derivatives undefined? 5. Where is this function increasing/decreasing and concave up/concave down? 6. Can the second derivative exist when the first derivative does not? Other times, it's easy to miss a critical or inflection point. You can usually detect something is wrong by using Rolle's Theorem, Mean Value The- orem, or Intermediate Value Theorem. If you've missed something, you can usually tell when you attempt to sketch the graph. For the following, attempt to sketch a graph with the properties listed, or explain why it's impossible. You may assume that the function and first two derivatives are continuous. 7. f'(1)-f (3) 0, f"(x) > 0 for 1 3 a < 3. 8. f'(x) > 0 for 0< < 3 and f"(1) 0 9. f"(0) = 1, f,(1) =-1, and f"(x) 〉 0 for 0 〈 x 〈 1.

Answer 1

paar方 Concave
6.If first derivative doesnt exist then second derivative also not exist