Questions: g'' is.... Select all that are True. sometimes positive always negative always positive called the "acceleration due to gravity" the same on every planet. different on every planet. called "gravity"

g'' is....
Select all that are True.
sometimes positive
always negative
always positive
called the "acceleration due to gravity"
the same on every planet.
different on every planet.
called "gravity"
Transcript text: $g^{\prime \prime}$ is.... Select all that are True. sometimes positive always negative always positive called the "acceleration due to gravity" the same on every planet. different on every planet. called "gravity"
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Solution

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Solution Steps

Step 1: Understanding the Question

The question asks about the second derivative of a function \( g \), denoted as \( g'' \). We need to determine which statements about \( g'' \) are true.

Step 2: Analyzing Each Statement
  1. Sometimes positive: This is true because the second derivative of a function can vary depending on the function itself. It can be positive in some intervals and negative in others.
  2. Always negative: This is not necessarily true. The second derivative can be positive, negative, or zero depending on the function.
  3. Always positive: This is not necessarily true for the same reason as above.
  4. Called the "acceleration due to gravity": This is incorrect. The acceleration due to gravity is a specific physical constant, often denoted as \( g \), not \( g'' \).
  5. The same on every planet: This is incorrect. The second derivative of a function is not related to planetary conditions.
  6. Different on every planet: This is also incorrect for the same reason as above.
  7. Called "gravity": This is incorrect. Gravity is a physical force, not a mathematical derivative.

Final Answer

\[ \boxed{\text{Sometimes positive}} \]

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