Find the Points on the Curve $y = 2 x ^ { 3 } + 3 x ^ { 2 } - 36 x + 19$

question 2

Multiple Choice

Find the points on the curve $y = 2 x ^ { 3 } + 3 x ^ { 2 } - 36 x + 19$ where the tangent is horizontal.

• A) \(( - 3,100 ) , ( 2 , - 25 )\)
• B) \(( - 3,88 ) , ( 4,39 )\)
• C) \(( - 4,71 ) , ( 4,39 )\)
• D) \(( - 4,71 ) , ( 2 , - 37 )\)
• E) \(( - 3,37 ) , ( 2 , - 37 )\)

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Definitions:

Graphing Calculator

A handheld calculator capable of plotting graphs, solving equations, and performing other complex mathematical tasks.

Vertex

A point where two or more curves, edges, or lines meet, often referring to the highest or lowest point on a curve.

Parabola

A specific type of curve on a graph described by a quadratic equation, characterized by being symmetrical and U-shaped.

Graph

A visual representation of data or a function using a system of coordinates.