Using Differentiation
i
Equation of tangent and normal
parallel
perpendicular I
Example 1
3
A curve C has equation y = (5 ¡ 2x)
Find the tangent to the curve at the point P with x-coordinate 1.
17 5 2 12 615 2 12
119941
3 2
1,3
6 5 2 172 54
12 1 1 1,227
54 X
Mton y y mean X
9 27 54 X 1
Example 2 54 54
4 27
A curve C has equation y = x ¡
³ ¼ ´5 2 y 54 81 0
sin x; 0 < x < ¼
2
Find the gradient of the curve at the point with x-coordinate
¼
4 5
4 2 costsinx
Ex 5 1 x E sinx x E
4
x E sinx 5 six 2 x E cost
E sine 5 sin 2 E cos
0 65
i
Equation of tangent and normal
parallel
perpendicular I
Example 1
3
A curve C has equation y = (5 ¡ 2x)
Find the tangent to the curve at the point P with x-coordinate 1.
17 5 2 12 615 2 12
119941
3 2
1,3
6 5 2 172 54
12 1 1 1,227
54 X
Mton y y mean X
9 27 54 X 1
Example 2 54 54
4 27
A curve C has equation y = x ¡
³ ¼ ´5 2 y 54 81 0
sin x; 0 < x < ¼
2
Find the gradient of the curve at the point with x-coordinate
¼
4 5
4 2 costsinx
Ex 5 1 x E sinx x E
4
x E sinx 5 six 2 x E cost
E sine 5 sin 2 E cos
0 65
