At the Given Point, Find the Slope of the Curve $y ^ { 5 } + x ^ { 3 } = y ^ { 2 } + 9 x$

question 266

Multiple Choice

At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve,
as requested.
- $y ^ { 5 } + x ^ { 3 } = y ^ { 2 } + 9 x$ , tangent at $( 0,1 )$

• A) \(y = - \frac { 9 } { 7 } x\)
• B) \(y = \frac { 9 } { 5 } x + 1\)
• C) \(y = 3 x + 1\)
• D) \(y = - \frac { 9 } { 5 } x - 1\)

---

Definitions:

Validity Assessment

The process of evaluating the extent to which a test or measurement accurately reflects or assesses the specific concept it is intended to measure.

Independent Variable

In research, a variable that is manipulated or changed by the researcher to determine its effect on another variable, called the dependent variable.

Control Group

In experimental research, a group of subjects that does not receive the experimental treatment and is used as a benchmark to measure the effect of the treatment on the experimental group.

Human Participants

Individuals who take part in research studies or experiments, contributing data through their actions, behaviors, or biological samples.