Differentiability

Differentiability - A. Sketch a graph of ( ) g r . Label...

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DIFFERENTIABILITY WORKSHEET 1. Use the graph of ( 29 2 ( ) 3 f x x x = + + to determine if '(0) f exists. Include a good sketch. 2. In each case, use the graph of ( ) f x to sketch a graph of '( ) f x . Label important features of '( ) f x and ( ) f x . Hint: Each function has some hidden features that you might not see on the standard window. Be careful. A. 2 3 ( ) 3 f x x x = - B. ( 29 1 3 ( ) 3 2 f x x x = + C. ( ) 28 13 5 f x x x = + - + - 3. The acceleration due to gravity, g , is a function of the distance from the center of the Earth, r . Let R be the radius of the Earth, M be the mass of the Earth, and G be the gravitational constant. 3 2 ( ) GMr r R R g r GM r R r < =
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Unformatted text preview: A. Sketch a graph of ( ) g r . Label important features. B. Is g a continuous function of r ? Explain. C. Is g a differentiable function of r ? Explain. 4. Find values for m and b so that ( ) g θ is differentiable at = . sin(2 ) ( ) g m b ≤ = + 5. Use the definition of the derivative to determine if '(0) f exists in each case. A. 2 1 sin ( ) x x f x x x ≠ = = B. 1 sin ( ) x x f x x x ≠ = =...
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This note was uploaded on 04/02/2008 for the course MATH 124 taught by Professor Kennedy during the Spring '08 term at Arizona.

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