8/6/2010 Assignment Previewer
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1 Week 4 Friday Homework ( ) Question Question DetailsSCalcET [ ] Consider te parabola y 7x - x 2. (a) Find te slope of te tangent line to te parabola at te point (1, 6). (b) Find an equation of te tangent line in part (a). y 2. Question DetailsSCalcET [ ] Find an equation of te tangent line to te curve at te point (-1, -1). y 4x 3-3x y 3. Question DetailsSCalcET MI. [ ] Find an equation of te tangent line to te curve at te point (49, 7). y x y Tutorial 4. Question DetailsSCalcET [ ] Consider te following curve. y 1 + 4x 2-2x 3. (a) Find te slope of te tangent to te curve at te point were x a. m (b) Find te equation of te tangent line at te point (1, 3). f(x) (c) Find te equation of te tangent line at te point (2, 1). g(x) webassign.net/ /control.pl 1/10
2 5. Question DetailsSCalcET [679818] A particle starts by moving to te rigt along a orizontal line; te grap of its position function is sown. (Coose all tat apply.) (a) Wen is te particle moving to te rigt? (0, 1) (1, 2) (2, 3) (3, 4) (4, 6) (b) Wen is te particle moving to te left? (0, 1) (1, 2) (2, 3) (3, 4) (4, 6) (c) Wen is te particle standing still? (0, 1) (1, 2) (2, 3) (3, 4) (4, 6) 6. Question DetailsSCalcET [ ] Find an equation of te tangent line to te grap of y g(x) at x 5 if g(5) 3 and g'(5) 4. y If te tangent line to y f (x) at (4, 7) passes troug te point (0, 6), find f(4) and f '(4). f (4) f '(4) webassign.net/ /control.pl 2/10
3 7. Question DetailsSCalcET [ ] Consider te function below. G(x) 2x 2 - x 3 (a) Find G ' (a). (b) Use te answer from part (a) to find an equation of te tangent line to te curve y G(x) at te point (2, 0). y (c) Use te answer from part (a) to find an equation of te tangent line to te curve y G(x) at te point (3, -9). y 8. Question DetailsSCalcET MI. [ ] Find f '(a). f(t) 4t + 20 t + 9 f '(a) Tutorial 9. Question DetailsSCalcET [679858] Te limit represents te derivative of some function f at some number a. Select an appropriate f(x) and a. f(x) x 5, a 2 f(x) x 6, a 1 f(x) x 7, a 0 f(x) x 6 - x, a 1 f(x) x 6 + x, a Question DetailsSCalcET [679822] Te limit represents te derivative of some function f at some number a. Select an appropriate f(x) and a. f(x) 4 x, a 16 f(x) 4 x, a 2 f(x) 2 x, a 4 f(x) x 4, a 2 f(x) 2 x, a Question DetailsSCalcET [679927] Te limit represents te derivative of some function f at some number a. Select an appropriate f(x) and a. f(x) cos(x), a π f(x) sin(x), a π f(x) tan(x), a π f(x) cos(x), a π/4 webassign.net/ /control.pl 3/10
4 12. Question DetailsSCalcET6 2.8.AE.02. [ ] EXAMPLE 2 (a) If f(x) 3x 3-5x, find a formula for f '(x). (b) Illustrate by comparing te graps of f and f '. SOLUTION (a) Wen computing a derivative, we must remember tat te variable is and tat x is temporarily regarded as a constant during te calculation of te limit. f '(x) f(x + ) - f(x) [3( ) 3-5(x + )] - [3x 3-5x] Video Example Online Textbook 3x x - 5-3x 3 + 5x ( + 9x ) (b) We use a graping device to grap f and f ' in te figure. Notice tat f '(x) 0 wen f as orizontal tangents, and f '(x) is positive wen te tangents ave positive slope. So tese graps serve as a ceck on our work in part (a). 13. Question DetailsSCalcET6 2.8.Tut.01. [697557] webassign.net/ /control.pl 4/10
5 14. Question DetailsSCalcET6 2.8.AE.05. [ ] EXAMPLE 5 Were is te function f(x) x - 8 differentiable? SOLUTION If x > 8, ten x - 8 and we can coose small enoug tat x > 0 and ence x terefore, for x > 8 we ave f '(x) x x - 8 and so f is differentiable for any x >. Similarly, for x < 8 we ave x - 8 and can be cosen small enoug tat x < and so x + - Video Example 8. Terefore for x < 8, Online Textbook f '(x) x x and so f is differentiable for any x < 8. For x 8 we ave to investigate f '(8) f(8 + ) - f(8) if it exists. Let's compute te left and rigt and limits separately: Since tese limits are different, f '(8) does not exist. A formula for f ' is given by and its grap is sown in te figure. Te fact tat f '(8) does not exist is reflected geometrically in te fact tat te curve y x - 8 does not ave a unique tangent line at (8, 0). webassign.net/ /control.pl 5/10
6 15. Question DetailsSCalcET [795719] Use te given grap to estimate te value of eac derivative. (Round all answers to one decimal place.) (a) f ' (-3) (b) f ' (-2) (c) f ' (-1) (d) f ' (0) (e) f ' (1) (f) f ' (2) (g) f ' (3) 16. Question DetailsSCalcET MI. [ ] Te graps of four derivatives are given below. Matc te grap of eac function in (a)-(d) wit te grap of its derivative in I-IV. I II III IV (a)? (b)? (c)? (d)? Tutorial webassign.net/ /control.pl 6/10
7 17. Question DetailsSCalcET [795717] Te grap of a function f is given. Select te grap of f '. webassign.net/ /control.pl 7/10
8 18. Question DetailsSCalcET [795742] Te grap of a function f is given. Select te grap of f '. webassign.net/ /control.pl 8/10
9 19. Question DetailsSCalcET [795738] Te grap of a function f is given. Select te grap of f '. webassign.net/ /control.pl 9/10
10 20. Question DetailsSCalcET [795723] Te grap of a function f is given. Select te grap of f '. Assignment Details Name (AID): Week 4 Friday Homework ( ) Submissions Allow ed: 5 Category: Homework Code: Locked: No Autor: Jernigan, Jon ( jjernigan@ccp.edu ) Last Saved: Jul 24, :10 PM EDT Permission: Protected Randomization: Person Wic graded: Last Feedback Settings Before due date Question Score Assignment Score Publis Essay Scores Question Part Score Mark Add Practice Button Help/Hints Response Save Work After due date Question Score Assignment Score Publis Essay Scores Key Question Part Score Solution Mark Add Practice Button Help/Hints Response webassign.net/ /control.pl 10/10
8/6/2010 Assignment Previewer
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