Which of the Following Properties Are Satisfied by the Following $\left\{ \begin{array} { l l } x ^ { 2 } + 1 & \text { for } x < 0 \\1 & \text { for } x = 0 \\5 x + 1 & \text { for } x > 0\end{array} \right.$

question 161

Multiple Choice

Which of the following properties are satisfied by the following function: f(x) = $\left\{ \begin{array} { l l } x ^ { 2 } + 1 & \text { for } x < 0 \\1 & \text { for } x = 0 \\5 x + 1 & \text { for } x > 0\end{array} \right.$ (I) f(x) is continuous
(II) f(x) is differentiable for all x
(III) f(x) is differentiable at x = -2

• A) III only
• B) I only
• C) I, II, and III
• D) I and II only
• E) I and III only

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Definitions:

Project Profitability Index

The ratio of the net present value of a project’s cash flows to the investment required.

Internal Rate

Typically refers to the Internal Rate of Return (IRR), a financial metric used to estimate the profitability of potential investments.

Discount Rate

The interest rate used in discounted cash flow analysis to determine the present value of future cash flows.

Payback Method

A capital budgeting technique that calculates the time required to recoup the cost of an investment.