Mathematics Homework Help

I’m studying for my Calculus class and need an explanation.

Determine whether each of the following statements is true or false, and explain why.

1. The absolute maximum of a function always occurs where the derivative has a critical number.
2. A continuous function on a closed interval has an absolute maximum and minimum.
3. A continuous function on an open interval does not have an absolute maximum or minimum.
4. Demand for a product is elastic if the elasticity is greater than 1.
5. Total revenue is maximized at the price where demand has unit elasticity.
6. Implicit differentiation can be used to find dy/dx when x is defined in terms of y.
7. In a related rates problem, all derivatives are with respect to time.
8. In a related rates problem, there can be more than two quantities that vary with time.
9. A differential is a real number.
10. When the change in x is small, the differential of y is approximately the change in y.