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problems on tangents, velocity, derivatives, and differentiation

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems A rock is thrown upward with a velocity of 10m/s, its height in meters t seconds later is given by. 1

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems 1-a 1-b Estimate the instantaneous velocity when. Find the average velocity over the given time intervals. (i) (ii) (iii)

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems The table shows the position of a cyclist. t(seconds)012345 s(meters)01.45.110.717.725.8 2 2-a 2-b Estimate the instantaneous velocity when. Find the average velocity for each time period. (i) (ii) (iii)

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems 3 The graph of a function and that of its derivative is given. Which is which?

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems Find the derivative of the functions below using the definition of the derivative. 4 4-a 4-c 4-e 4-b 4-d

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems State, with reasons, the numbers at which f is not differentiable. 5

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems Find the equation of the line tangent to the graph of the function at the point. Find all points on the graph of the function at which the tangent line is horizontal. 6 7

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems 8 8-a 8-b Do the following functions have derivative at ? 8-c

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems 9 10 Assume that f has derivative everywhere. Set. Using the definition of derivative, show that g has a derivative and that. Show that the function is differentiable everywhere.

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Mika Seppälä: Problems on Tangents, Velocity, Derivatives, and Differentiation overview of problems 11 Show that f is differentiable at.

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3.2 & 3.3. State the Differentiability Theorem Answer: If a function is differentiable at x=a, then the function is continuous at x=a.

3.2 & 3.3. State the Differentiability Theorem Answer: If a function is differentiable at x=a, then the function is continuous at x=a.

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