Consider the Differential Equation $y ^ { \prime }$ = G(y) Where G(y) Is the Function Whose Graph Is

question 122

Multiple Choice

Consider the differential equation $y ^ { \prime }$ = g(y) where g(y) is the function whose graph is shown below:
Indicate whether the following statements are true or false.
-Let $y ^ { \prime }$ = $y ^ { 3 }$ . Which of the following properties hold for the solution y = f(t) determined by the initial condition y(0) = -2? (I) It is always increasing.
(II) It has an inflection point.
(III) It is always concave down.

• A) I only
• B) I and II
• C) II only
• D) III only
• E) none of these

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Definitions:

Evidence

Information or facts that are used to support a conclusion, claim, or belief.

Personally Relates

A term denoting the direct connection or relevance one has with a particular situation, topic, or experience.

Dynamism

The quality of being dynamic, characterized by constant change, activity, or progress.

Ethics

Moral principles that govern a person's behavior or the conducting of an activity, often serving as a guide for what is considered right or wrong.