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 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) 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

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

Tangent to a curve

The gradient of the distance time graph is the speed.

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