Determine Whether Each of the Following Statements Is True or False

question 82

Essay

Determine whether each of the following statements is true or false. If the statement is true, provide an appropriate justification. If the statement is false, provide a counterexample.(a) If $f ( x ) \neq 0 \text { on } [ a , b ] \text { then } \int _ { a } ^ { b } f ( x ) d x \neq 0$ (b) If $f$ is continuous on an interval containing a,b, and c, then $\int _ { a } ^ { b } f ( x ) d x = \int _ { a } ^ { c } f ( x ) d x - \int _ { b } ^ { c } f ( x ) d x$ (c) If $\int _ { a } ^ { b } f ( x ) d x \geq 0 , \text { then } f ( x ) \geq 0 \text { on } [ a , b ]$

---

Definitions:

Maximum Return

The highest possible profit or gains that can be achieved from an investment or business venture.

Income From Operations

The profit realized from a business's ongoing operations, excluding any income derived from investments or extraordinary one-time events.

Residual Income

The amount of income that remains after all personal debts and expenses have been paid.

Minimum Acceptable

The lowest level or standard that is satisfactory or allowable.