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  # 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)

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