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Bài tập CALCULUS 48
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Created by T. Madas
Question 173
(****)
y=3x+
27
, x ≠ 0.
x
Find the range of values of x for which y is increasing.
MP1-D , x > 27
Created by T. Madas
Created by T. Madas
Question 174
(****)
The points ( −2, −1) and (1, −4 ) lie on the curve C with equation y = f ( x ) .
The gradient function of C is given by
dy
= 3x 2 + 4 x + k ,
dx
where k is a constant.
a) Find an equation of C , in the form y = f ( x ) .
The straight line L has equation
y = −3 x − 5 .
b) Show that L is a tangent to C and determine further the coordinates of the
point of tangency.
C1O , y = x3 + 2 x 2 − 2 x − 5 ,
Created by T. Madas
( −1, −2 )
Created by T. Madas
Question 175
(****)
y
O
C
x
L2
L1
L3
The figure above shows the curve C with equation
2 x4 − x + 6
, x ≠ 0.
y=
6x
The straight line L1 has equation 4 y = 15 x .
The straight lines L2 and L3 are tangents to C .
Given that L1 , L2 and L3 are parallel to one another, determine an equation of L2 and
an equation of L3 .
C1V , 4 y = 15 x − 18 or y = 15 x − 9 , 12 y = 45 x + 50 or y = 15 x + 25
4
2
4
6
Created by T. Madas
