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A test paper for a calculus course, consisting of multiple-choice questions and problems requiring differentiation and optimization. Students are required to solve each problem, showing all the work to justify their answers. The exam lasts for one and a half hours and covers topics such as differentiation, limits, and optimization.
Typology: Exams
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You have one and half hours to complete this examination. Write your answers directly on the exam paper. If you need extra space, use the back of the page and indicate on the front that you have done so. Use of calculator is allowed for Part II only. No other reference materials are allowed. You must give a complete solution to each problem, showing all the work necessary to justify your final answer. The entire solution, not just the answer, will be graded, and partial credit is possible. A correct final solution will not, of itself, guarantee full credit. Total Points: 104 points
Use appropriate rules and formulas to differentiate (or to find dx dy ) of each function.(4pts each)
(^) x x e e f x
a) ( 4 pts)Find all critical points for f^ ( x ). b) ( 4 pts)Find all inflection points for f^ ( x ), if any.