1. Find the equation of the tangent line for y = x2 + 6 at x = 3
Note: The following examples are part of sections homework
Find the equation of the tangent line for y = x at x = 3
Solution:
The slope of the tangent line at any point is the derivative at that point
y' = 2 x
At x = 3, we need to find m and y : 3
x = 3 then m =y' (3) = 2(3) = 6
x = 3 then y(3) = (3)2 + 6 = 15 15
Now we want to find the equation of the line
that passes the point (x =3, y =15) with m = 6
y = mx + b
15 = (6)(3) + b
-3 = b
The equation of the tangent line at x = 3 is: y = 6x - 3

2. The equation of the tangent line at x = 2 is: y = 10x - 15
Find the equation of the tangent line for y = x3 - 2x + 1 at x = 2
Solution:
The slope of the tangent line at any point is the derivative at that point
y' = 3x2 - 2
At x = 2, we need to find m and y :
x = 2 then m =y' (2) = 3(2)2- 2 = 10 5
x = 2 then y(2) = (2)3 -2(2) + 1= 5
Now we want to find the equation of the line
that passes the point (x = 2, y = 5) with m = 10
y = mx + b
5 = (10)(2) + b
-15 = b
The equation of the tangent line at x = 2 is: y = 10x - 15