MS125-01 Test 2: Calculus Examination October 2006, Exams of Calculus

Download MS125-01 Test 2: Calculus Examination October 2006 and more Exams Calculus in PDF only on Docsity! MS125-01 Test 2 (Oct. 25, 2006) NAME: __________________________ 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 Part I Use appropriate rules and formulas to differentiate (or to find dx dy ) of each function.(4pts each) 1. 42 )15()(  xxxf 2. 2)31()( xexf  3. xxxf 3sin)( 2 4. xxf 2tan)(  5. )arctan()( 3ttg  6. 3323  yxyx 7. )cosh(sin)( xxf  8. 1 1 )(    x x e e xf Part II 1. Let 24)( 1   xexf x be a one-to-one function. a) (3pts)What is )3(1f ? b) (4pts)Evaluate )3()( 1 f ? 2. Let xxxf cos2)(  on  2,0 . a) (4pts)Find all critical points for )(xf . b) (4pts)Find all inflection points for )(xf , if any.