$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$

question 314

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $$y ^ { 2 } - x ^ { 2 } = 4$$

• A) \(\frac { \mathrm { dy } } { \mathrm { dx } } = - \frac { \mathrm { x } } { \mathrm { y } } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } ^ { 2 } } = \frac { \mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } } { \mathrm { y } ^ { 3 } }\)
• B) \(\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { \mathrm { x } } { \mathrm { y } } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } 2 } = \frac { \mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } } { \mathrm { y } ^ { 2 } }\)
• C) \(\frac { d y } { d x } = \frac { x } { y } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { y ^ { 2 } - x ^ { 2 } } { y ^ { 3 } }\)
• D) \(\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { \mathrm { x } } { \mathrm { y } } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } \mathrm { x } ^ { 2 } } = \frac { \mathrm { y } - \mathrm { x } ^ { 2 } } { \mathrm { y } ^ { 2 } }\)

Apply the payback method in evaluating the profitability and risk of investments.

Use real-options analysis and other scenario-based methods in capital budgeting.

Understand the concept of and distinguish between various capital budgeting techniques.

Apply the net present value (NPV) method to evaluate investment projects.

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Definitions:

Normal Balance

The account side (either debit or credit) that documents the account's increases, based on the type of account.

Financial Statement

Official documentation of a business, individual, or entity's financial transactions and status.

Permanent/Temporary

Classification of employees or work status based on duration of employment, with permanent indicating long-term employment and temporary indicating short-term engagements.

Unemployment Merit Tax Rate

A tax rate assigned to businesses based on their history of unemployment claims filed by former employees, affecting the state unemployment tax rate.