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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) 
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 
The gradient is defined by the RISE divided by the RUN 

Mouse over graph 

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) 