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

question 385

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $x ^ { 2 } + y ^ { 2 } = 5$ , at the point $( 2,1 )$

• A) \(\frac { d y } { d x } = - 2 ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = 1\)
• B) \(\frac { d y } { d x } = 2 ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = 5\)
• C) \(\frac { \mathrm { dy } } { \mathrm { dx } } = - \frac { 1 } { 2 } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } ^ { 2 } } = 0\)
• D) \(\frac { d y } { d x } = - 2 ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = - 5\)

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Definitions:

Non-Experimental Methods

Research techniques that do not involve the manipulation of variables, often used to study associations between variables rather than causal relationships.

Archival Research

Non-experimental method involving the assembly of data, or reports of data, collected by others.

Case Studies

Detailed examinations of a single subject or entity, often used in psychology, sociology, and business to analyze complex issues or dynamics.

Field Experiments

Research studies conducted in natural, real-life settings outside the laboratory to understand the impact of variables in a more natural context.