Bài tập CALCULUS 20

Created by T. Madas
Question 79

(***)

The curve C has equation

y = x 4 − 2 x3 + 1 , x ∈ » .
Find the coordinates of the stationary points of C and determine their nature.

(

)

C2Q , min at 3 , − 11 , point of inflexion ( 0,1)
2 16

Created by T. Madas


Created by T. Madas
Question 80

(***) non calculator

The curve C has equation
y = x2 −

16
3x 2

, x ≠ 0.

Show that C has two points of inflection and determine their coordinates.

( 2, 83 ) , ( −2, 83 )

Created by T. Madas


Created by T. Madas
Question 81

(***)
2

 2x +1
y =
 , x >0.
 3x 2 
a) Express y in the form Ax −2 + Bx −3 + Cx −4 , where A , B and C are fractions
to be found.
b) Hence determine simplified expressions for …
i. …

dy
.
dx

ii. …



y dx

dy
C1K , y = 4 x −2 + 4 x −3 + 1 x −4 ,
= − 8 x −3 − 4 x −4 − 4 x −5 ,
9
9
9
9
3
9
dx



y dx = − 4 x −1 − 2 x −2 − 1 x −3 + C
9
9
27

Created by T. Madas