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Read before you complete this assignment!

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Read before you complete this assignment!

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As you read section 3.2, note any questions or comments you have about the text. What do you notice? What do you wonder? Post them under their relevant headings. You are encouraged to upvote questions or comments you also have, but that does not count as your unique question(s) or comment(s). You are also encouraged to respond to your peers, but always remember to be kind and instructive!

To exceed the standard on this homework, do some research around and post a resource relevant to the last column titled "Average vs Instantaneous Rate of Change".

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Does this mean that the entire function doesn’t have a derivative, or just a single point?

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How can you tell if a function will not have a derivative at a certain point without graphing it?

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If “corner” functions are continuous how come they don't have a derivative at a certain point?

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https://www.youtube.com/watch?v=J7VbhV_yp2U

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So basically because the 2 points you use when finding the derivative are so close together the line they form is seen as linear?

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So differentiability is where a functions derivative exists at each point in the domain. If a function is differentiable at a point then it must be continuous at that same point. So basically if a function is differentiable it must also be continuous and if it is continuous it must be differentiable?

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https://www.khanacademy.org/math/in-in-grade-11-ncert/in-in-class11-derivatives/copy-of-derivative-as-instantaneous-rate-of-change-ab/v/approximating-equation-of-tangent-line-word-problem-1

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When one of the derivative fails to exist, does the other one also fail to exist? Or just that one. (Right hand and left hand)

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When one of the derivative fails to exist, does the other one also fail to exist? Or just that one. (Right hand and left hand)

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-Julian

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https://www3.nd.edu/~apilking/Math10560/Calc1Lectures/6.%20Derivatives%20and%20Rates%20of%20Change.pdf

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If a function does have a cusp, corner, or vertical tangent lines, are they automatically undefined

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If a function does have a cusp, corner, or vertical tangent lines, are they automatically undefined

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-Julian

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Does this mean that a derivative can only be one line? or can there be multiple lines in one derivative

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Does this mean that a derivative can only be one line? or can there be multiple lines in one derivative

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Julian

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What is the actual definition of differentiability?
-Joe

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what is the point of the difference quotient if the symmetric difference quotient is more accurate?
-Joe

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Is there a way to tell if a function has a cusp, corner, or vertical tangent without the graph?

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Is there a way to tell if a function has a cusp, corner, or vertical tangent without the graph?

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What is the difference between differentiability and continuity

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What is the difference between differentiability and continuity

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Although you have to sign in after a bit this ones talks about it in the beginning

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If f doesn't have a derivative at x=a then is x=a not continuous?

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If a and b are two points on an interval where f is not differentiable, then can f still takes
on every value between fa and fb?

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Would the degree of a function indicate whether its derivative exists?

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Would the degree of a function indicate whether its derivative exists?

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How can you define differentiability as it relates to derivatives?

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How can you define differentiability as it relates to derivatives?

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Can functions be differentiable if they have a removable discontinuity?

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Can functions be differentiable if they have a removable discontinuity?

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Do the same general rules of continuity, outlined in the intermediate value theorem, apply to derivatives?

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Do the same general rules of continuity, outlined in the intermediate value theorem, apply to derivatives?

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Does the degree of a function affect the derivative and could it cause f(a) not to exist?

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Does the degree of a function affect the derivative and could it cause f(a) not to exist?

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-Evan

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Didn't really fit into any category, but why don't you use .1, .01, .001 in the calculator?

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Didn't really fit into any category, but why don't you use .1, .01, .001 in the calculator?

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-Evan

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Can we go over this in class? Really confused.

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Can we go over this in class? Really confused.

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-Evan

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Graphs 1-3 all show the lines being continuous at (0,0), if the y intercept changed, would f'(a) still not exist?

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Graphs 1-3 all show the lines being continuous at (0,0), if the y intercept changed, would f'(a) still not exist?

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Will we learn how to do this on our calculators or learn a different method of finding tangents?

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What is the Unit Step Function?

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It's not a link but some of us have the book "Physics for Scientists and Engineers" which talks about this on pages 21-27 (Sections 2.1 and 2.2)

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(The graph changes dramatically, basically. Corners, cusps, discontinuities, and where there is no slope (because the tangent of the location will not be able to be calculated because no slope)²

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(f a derivative can be found, it is continuous at that point. It has to be, because if it wasn't continuous there'd be no derivative.)²

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It's like if you play the triangle in an orchestra and you mess that up

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It's like if you play the triangle in an orchestra and you mess that up

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(Is this just like the continuity thing when if theres two points and its continuous between them but for derivatives?)²