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

question 475

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $x y + 3 = y$ , at the point $( 4 , - 1 )$

• A) \(\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { 1 } { 3 } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } { } ^ { 2 } } = \frac { 2 } { 9 }\)
• B) \(\frac { d y } { d x } = 3 ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = - 24\)
• C) \(\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { 1 } { 3 } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } ^ { 2 } } = - \frac { 2 } { 9 }\)
• D) \(\frac { d y } { d x } = - \frac { 1 } { 3 } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = 0\)

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Definitions:

Linearly Related

Describes the direct proportional relationship between two variables, where a change in one variable is associated with a consistent change in another.

Least Squares Line

A line of best fit through a scatter plot of data points that minimizes the sum of the squares of the vertical distances of the points from the line.

Least Squares Line

A straight line that minimizes the sum of the squares of the vertical distances of the points from the line.

Y-intercept

The point where a line or curve crosses the y-axis of a graph, representing the value when all independent variables are zero.