1. Gradient of a Curve: this is given by the gradient of the tangent
Find the gradient of
y = x2 - 3x - 2 at the point x = 3
(5,4)
Use the table feature on your calculator to get a table of values and plot the graph x y -3 16 -2 8 -1 2 1 -4 3 4 5
Draw a tangent at the
point x = 3
Select 2 points on your tangent line
(2,-5)

2. Gradient of a Curve: this is given by the gradient of the tangent
Find the gradient of
y = x2 - 3x - 2 at the point x = -1
(-1.5,4)
Draw a tangent at the
point x = -1
Select 2 points on your tangent line
(0,-3.5)

3. Finding the Equation of the tangent
Find the equation of the tangent to
y = x2 - 3x - 2 at the point x = 3
Using y = mx + C
From slide 1
m = 3 and x = 3
To find y use the equation y = x2-3x-2 with x = 3
y = 32-33-2 = -2
So y = -2

4. Finding the Equation of the tangent
Find the equation of the tangent to
y = x2 - 3x - 2 at the point x = 3
Using y = mx + C
m = 3 and x = 3 , y = -2
y = 3x-11
Using y = mx + C
-2 = 33 + C
-2 = 9 + C
Forwards C + 9 = -2
Backwards = C
C = -11
So the equation of the tangent is y = 3x-11

5. Checking on the calculator
Enter y1 = x2-3x-2 and y2 = 3x-11
Now do the questions on pg 30 in your notes