True/False

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salma

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Nov 28, 2012
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Im doing a study guide and wanted to make sure I got these right. (true or false)

1) The average rate of change between two points gives us the slope of
the tangent line between those two points. FALSE


2) The derivative evaluated at a point gives us the slope of the secant line T F
at that point. TRUE


3) The derivative of a product can be found by multiplying the
derivatives of each part of the product together. TRUE


4) The derivative of π^2 is 2π. TRUE


5) The derivative of a linear function is a constant. FALSE

..am I correct?
 
salma said:
Im doing a study guide and wanted to make sure I got these right. (true or false)

1) The average rate of change between two points gives us the slope of
the tangent line between those two points. FALSE - This question does not make sense to me. Tangent line exists at a point - secant line exists between two points.


2) The derivative evaluated at a point gives us the slope of the secant line T F
at that point. TRUE - false - derivative gives us the slope of the tangent line at that point.


3) The derivative of a product can be found by multiplying the
derivatives of each part of the product together. TRUE - False


4) The derivative of π^2 is 2π. TRUE - false The derivative of π^2 is 0


5) The derivative of a linear function is a constant. FALSE incorrect - true

..am I correct?
Click to expand...
.
 
Thats how its written on my study guide.Im just going with false.
 
salma said:
Im doing a study guide and wanted to make sure I got these right. (true or false)

1) The average rate of change between two points gives us the slope of
the tangent line between those two points. FALSE
Click to expand...
I HATE True/False tests.

Answer true or false: Unicorns trust maidens.

I don't know because unicorns do not exist.

As Subhotosh Khan AND mmm pointed out, the question makes no sense. A tangent line is defined with respect to a POINT on a curve. I presume that the answer desired by a math teacher to a math question that makes no sense at all is FALSE, but who can be sure.
 
I would interpret that as "if x is unicorn, then x trusts maidens". And since the hypothesis is false, the entire statement is true.

As for "1) The average rate of change between two points gives us the slope of the tangent line between those two points", yes, a tangent line is determined by a single point and the statement is false, in general. What's true is that "The average rate of change between two points gives us the slope of the secant line between those two points.
 
I suspect you risk commitment if you insist on the truth of the unadorned statement that "unicorns trust maidens" because it is just as sensible to interpret the statement as "unicorns, which do exist, trust maidens" (FALSE) as to interpret it as "if unicorns existed, they would trust maidens" (INDETERMINATE) or as "if x is a unicorn, x trusts maidens" (TRUE). And that is my whole point: a question that makes no sense invites different interpretations, and a true/false dichotomy allows no opportunity to give an answer that is contingent on the interpretation of the question.
 
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