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Homework 6 Differentiation
Your Score:
1)
a)
y = x
2
–
8 x + 12
dy / dx =
b)
y = 6 x
6
+
2 x
-6
–
7 x
dy / dx =
c)
y = 5 x
2
+
9 x
-2
+ 6 x
3
+ 4 x
dy / dx =
d)
y = -4 x
-2
–
9 x
-3
+ 6 x
3
+ 2 x
dy / dx =
e)
y =
–
x
-1
+
x
1
+ x
2
–
2 x
-2
dy / dx =
Q2)
Calculate the gradient of the following functions at the point given:
a)
gradient of
y = 3 x
2
+ 5 x + 7
at
x = -6
b)
gradient of
y =
–
2 x
2
–
3 x + 14
at
x = -2
c)
gradient of
y =
2
x
-2
+
2 x
3
–
5 x
at
x = 2
d)
gradient of
y =
3
x
3
–
3 x
-3
–
3 x
at
x = -2
Q3)
y =4x³-2x²+2x+6
a)
Find the equation of the tangent to the curve above at:
x =2
y =
x +
b)
Find the equation of the normal to the curve at:
x = 0
y =
x +
Q4)
y = 2
x
3
+ 9 x
2
–
108 x
+
6
dy / dx =
Find the location of the two turning points:
A
B
x
1
=
x
2
=
y
1
=
y
2
=
Fill in the tables below:
A
B
x
x
dy/dx
dy/dx
Hence determine the nature of the turning points: "max" or "min":
Nature of turning point A:
Nature of turning point B:
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