MATH 1050 Salt Lake Community College Intermediate Value Theorem Paper

Hi i need help with my homework if you could show work so i understand how it is done.

Math 1050 HW #4 – Sections 2.1 and 2.2
Name: ____________________________________
Please show all of your work. Scan your solutions into a pdf file and upload it into the homework assignment.
1. Use the Intermediate value theorem to show that H ( x)  x1000  x  3 has a root on [0, 2] .
2. Find a function that could be represented by this graph:
3. Why must every polynomial of odd degree have at least one zero?
4. Can an x-intercept of a polynomial function yield a local maximum or local minimum? Verify with a sketch or
explanation.
5. Can an x-intercept of a polynomial function yield an absolute maximum or absolute minimum? Verify with a
sketch or explanation.