Differentiation From First Principles
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Transcript of Differentiation From First Principles
Finding the Gradient of the Tangent
Finding the Gradient of the Tangent: Group 1
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
1
Gradient of the line joining to
1
Gradient of the line joining to
1
Gradient of the line joining to
1
Do the gradients seem to be getting closer and closer to a particular number?(Try another one if youre not sure)
We think the gradient of at is
Finding the Gradient of the Tangent: Group 2
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
2
Gradient of the line joining to
2
Gradient of the line joining to
2
Gradient of the line joining to
2
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is Finding the Gradient of the Tangent: Group 3
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
-1
Gradient of the line joining to
-1
Gradient of the line joining to
-1
Gradient of the line joining to
-1
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is Finding the Gradient of the Tangent: Group 4
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
-2
Gradient of the line joining to
-2
Gradient of the line joining to
-2
Gradient of the line joining to
-2
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is Finding the Gradient of the Tangent: Group 5
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
0
Gradient of the line joining to
0
Gradient of the line joining to
0
Gradient of the line joining to
0
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is Finding the Gradient of the Tangent: Group 1
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
1
Gradient of the line joining to
1
Gradient of the line joining to
1
Gradient of the line joining to
1
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is
Finding the Gradient of the Tangent: Group 2
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
2
Gradient of the line joining to
2
Gradient of the line joining to
2
Gradient of the line joining to
2
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is Finding the Gradient of the Tangent: Group 3
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
-1
Gradient of the line joining to
-1
Gradient of the line joining to
-1
Gradient of the line joining to
-1
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is Finding the Gradient of the Tangent: Group 4
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
-2
Gradient of the line joining to
-2
Gradient of the line joining to
-2
Gradient of the line joining to
-2
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is Finding the Gradient of the Tangent: Group 5
We are going to try to find the gradient of the tangent to the curve at (blue line) by looking at the gradients of the lines joining to , then , then etc to see if we can spot a pattern.
What are we looking for?
Gradient
Gradient of the line joining to
0
Gradient of the line joining to
0
Gradient of the line joining to
0
Gradient of the line joining to
0
Do the gradients seem to be getting closer and closer to a particular number?
(Try another one if youre not sure)
We think the gradient of at is Table for results1.Curve
x valueGradient
-2
-1
0
1
2
We think the rule for the gradient is:Gradient =
2.Curve
x valueGradient
-2
-1
0
1
2
We think the rule for the gradient is:Gradient =
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