Explain the difference between a local and an absolute

Question

1.  Explain the difference between a local and an absolute maximum. Are extrema x values or y values?

2. If an odd function f has one local maximum of 5 at x = 3, then what else can be said about f? Explain.

3. If an even function f has an absolute minimum of -6 at x = -2; then what else can be said about f? Explain.

4. Explain how to determine graphically whether a zero of a polynomial is a multiple zero. Sketch examples.

5. Show that the following equation has no rational roots. Explain how you did it.

x⁵ - x⁴ - x³ + x² - 2x + 3 = 0

6. Could a cubic function with real coefficients have only imaginary zeros? Explain

7. Give an example of a polynomial function that has only imaginary zeros and a polynomial function that has only real zeros. Explain how to determine graphically if a function has only imaginary zeros.