The Slope F '(X)at Each Point (X,y)on a Curve Y $f ^ { \prime } ( x ) = x e ^ { 36 - x ^ { 2 } }$

question 14

Multiple Choice

The slope f '(x) at each point (x,y) on a curve y = f (x) is given,along with a particular point (a,b) on the curve.Use this information to find f (x) . $f ^ { \prime } ( x ) = x e ^ { 36 - x ^ { 2 } }$ ; (-6,1)

• A) \(y = - 1 - \frac { 1 } { 2 } e ^ { 36 - x ^ { 2 } }\)
• B) \(y = - \frac { 1 } { 2 } e ^ { 3 - x ^ { 2 } }\)
• C) \(y = \frac { 3 } { 2 } - \frac { 1 } { 2 } e ^ { 36 - x ^ { 2 } }\)
• D) \(y = 1 - \frac { 1 } { 2 } e ^ { 36 - x ^ { 2 } }\)

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Definitions:

Flash Flooding

Rapid and extreme flow of high water into a normally dry area, or a rapid water level rise in a stream or creek above a predetermined flood stage, often caused by intense rainfall.

Mountain Ranges

Chains or clusters of mountains that are close together in a line or a group, often formed by tectonic forces or volcanism.

Flooding Hazards

Risks associated with excessive water, often due to heavy rainfall or river overflow, that can cause damage to structures and loss of life.

Mudslide Hazards

Risks associated with rapid downslope movement of soil and rock, often triggered by heavy rainfall or seismic activity.