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Gradient

Calculus HOME | Achievement Objectives | Gradient | Gradient Functions | Differentiation | Gradient at a point | Find point with gradient | Equation of Tangent | Second Derivitive | Coordinates of Max & Min | Increasing, Decreasing Functions | Applications | Kinematics with differentiation | Antidifferentiation | Finding 'C' | Kinematics with anti-differentiation | Rates of Change | Mixed Problems | Revision

1

Overview, gradient & Tangents

Topic Overview: Achievement Objectives,

Review of gradient of a line, what is a tangent

Finding the gradient of a curve at a point, tangents, turning points.

Calculus surfer - Thanks to Evelyn Knight for sourcing the link (homepages.gac.edu) Note: you need to remember to use * for anything multiplied, e.g. y = x*(x+1)*(x+2).

Key concept: Gradient of tangent = gradient of curve at a point

Demo of Gradient Function (enable macros)

Achievement Standard

Class Notes | Blank Notes

p66, 67

Introduction to differentiation and motion graphs link to www.mathsroom.co.uk

 

Animation of gradient of curve | vertical |at a corner

Web link to a cool Calculus Surfer

Gradient of a line segment

How steep is that?

click for a larger image

The gradient is defined by the RISE divided by the RUN

 

 

Mouse over graph
 for gradient calculation

Positive gradient uphill)
Negative gradient (downhill) 

How do we find the gradient (slope) of a curve?

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Tangent to a curve

Move the point on the curve. 
Note the tangent line and gradient change.
The gradient of the distance time graph is the speed.

Calculus surfer - Thanks to Evelyn Knight for sourcing the link (homepages.gac.edu)

If we zoom in on the point where the tangent touches the curve the gradients gets closer (tangent gradient approximate equal curve gradient)

Conclusion: At the point the gradient of the tangent of the tangent as the same as the gradient of the curve

Class Notes | Blank Notes Screen shots:

 

 

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