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Unformatted text preview: . [3] Answer 2 FULLSOLUTION PROBLEMS. In questions 2–4, justify your answers and show all your work. If you need more space, use the back of the previous page. 2. Carefully prove that 2 x 4x 3 + 2 x 21 has a root between x =1 and x = 1. [5] 3. Use the defnition of the derivative to prove that if f ( x ) is a diFerentiable function [6] and g ( x ) = x 2 f ( x ), then g ( x ) = x 2 f ( x ) + 2 x f ( x ). No credit will be given for using the Product Rule. 3 4. Find a point on the curve y = 16x 2 that is below the xaxis, such that the tangent [5] line through that point also passes through the point (5 , 0), or determine that no such point exists. 5. Let [6] f ( x ) = ( ax + b if∞ < x ≤ 2, c + ( x2) 2 sin ± 1 ( x2) 2 ² if 2 < x < ∞ , and determine all values (if any exist) of the constants a , b , and c so that f ( x ) is continuous for all x . (Remember to justify your answer.) 4...
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 Fall '10
 LIOR
 Calculus, Derivative

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