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