（C）global maximum （D）global minimum (15) Which of the following curves hasthe inflection point (0, 0) ? （ （A） y x
2
（B） y x
3
（C） y x
4
（D） y x
2 3
2. Find the Local maximum and minimum for y 2 x 3 6 x 2 18 x 7 . (10 pts.)
（C）is decreasing in (o, + )
(D) is increasing in（0, + ）
(10) If in (a, b) f ( x) 0 , f ( x) 0 , then y f ( x) is（ ）in (a, b) . （A）decreasing and convex up （B）decreasing and convex down （C）increasing and convex up （D）increasing and convex down (11) What are all values of x for which the function f defines by
（D） 1 , 0 , and 1
(13) If y ax 2 b is strictly increasing in (0 , ) ，then a , b should be satisfied（ ）. （A） a 0 , b 0 （B） a 0 , b R （C） a 0 , b 0 （D） a 0 , b R (14) 2 is the（ ）for y x 3 3 x 2 6 x 2 on [1, 1] . （A）local maximum （B）local minimum ）.
3. Find the intervals of concavity and convexity and the inflection points for y xe x . (10 pts.)
4. Prove the following inequalities: (2*10=20 pts.)
x 0
(A) local maxima (C) not local extreme (7)
(B) local minima (D) maybe local extreme
y x 3 12 x 1 （ ）in its domain.
（A） is increasing （B） is decreasing （C）is concave （D）is convex (8) If y f ( x) obtain local maximum at x x0 ，then it must be（ ）. （A） f ( x0 ) 0 （B） f ( x0 ) 0 （C） f ( x0 ) 0 且 f ( x0 ) 0 （D） f ( x0 ) = 0或 f ( x0 ) 不存在 (9) f ( x) x ln x （ ） 1 1 （A）is decreasing in (0, ) （B）is decreasing in ( ) e, e

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1
Test 4
Date___________ Class___________
Name___________ Score__________
ba f ( ) f (b) f (a ) f (b) f (a ) (C) f ( ) ba (3) If x 0 , then （ ）.
(A)
(B) f ( ) f (b) f (a ) (D) f ( ) f (a ) f (b)
(A) e x e x (B) e x x 1 (C) e x e( x 1) (D) ln(1 x) x (4) If y
Test 4
Date___________ Class___________
Name___________ Score__________
1. Choose the best answer for each question. (4*15 = 60pts.) (1) If f :[a, b] R, satisfies: (1) f is continuous on [a, b]; (2) f is differentiable on (a, b); (3) f (a) = f (b), then there exists at least one point (a, b) such that f ( ) （ ）. (A) 0 (B) 1 (C) f ( ) f (a ) (D) 1
x , then in the open interval (1 , 1) （ ）. 1 x2 （A）y is increasing （B）y has a relative maximum
（C）y is decreasing （D）y has a relative minmum (5) If f ( x ) xe x , then at x 1 （ ）. （A）f is increasing （B）f has a relative maximum （C）f is decreasing （D）f has a relative minmum (6) Let f ( x) continuous ，and f (0) = 0， lim f ( x) =1，then f (0) is （ ）value of f ( x) .
f ( x) x 3 3 x 2 9 x 7 is increasing? ( ).
（A） 3 x 1 （B） 1 x 1 （C） x 3 or x 1 （D） x 1 or x 3 (12) If f is the function defined by f ( x) 3 x 5 5 x 4 , what are all the x–coordinates of points of inflection for the graph of f ? ( （A） 1 （B） 0 and 1 （C） 1 ).
(1) tan x > x if x 0, . 2
(2) 1
1 x 1 x ( x 0) . 2
If you have found any mistakes in Test 4, please report them to your Math teacher !
(2) If f :[a, b] R, satisfies: (1) f is continuous on [a, b]; (2) f is differentiable on (a, b); then there exists at least one point (a, b) such that f ( ) （ ）.