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Bài tập CALCULUS 03
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Created by T. Madas
Question 8
(**)
The curve C has equation
y = x3 − x 2 − 5 x + 2 .
Find the x coordinates of the points on C with gradient 3 .
x = − 4 ,2
3
Created by T. Madas
Created by T. Madas
Question 9
(**)
y
y = x3 − 8 x 2 + 16 x
R
O
A
x
The figure above shows the cubic curve with equation
y = x3 − 8 x 2 + 16 x , x ∈ » .
The curve meets the x axis at the origin O and at the point A .
a) Show clearly that x = 4 at A .
The finite region R is bounded by the curve and the x axis.
b) Find the exact area of R .
C2N , 64
3
Created by T. Madas
Created by T. Madas
Question 10
(**)
The point P (1,3) lies on the curve with equation y = f ( x ) , whose gradient function is
given by
f ′ ( x ) = 6 x2 − 4 x , x ∈ » .
Find an equation for f ( x ) .
C1F , f ( x ) = 2 x3 − 2 x 2 + 3
Question 11
(**)
The curve C has equation
y = x5 − 6 x3 − 3x + 25 .
Find an equation of the tangent to C at the point where x = 2 .
y = 5x − 7
Created by T. Madas
