Section 31,32,33

Increasing and decreasing functions

Tangents and Normals

• The gradient of the tangent is equal to the gradient of the curve

• The normal is perpendicular to the tangent and has the formula: −1/ f’(x)

Stationary points

• f’(x) = 0

Second Derivatives

Point of inflection

• When the curve changes between being concave and convex

• If f’’’(x) does not equal zero it means the x value is a point of inflection

• To find the change in sign use the numbers 0.1 above and below the x value

• Write conclusion

Numerical Methods - Sign change method for locating roots

• Substitute numbers given into f(x) to see change in sign

• Prove roots by using lower and upper bounds of number given

Newton raphson method

Addition Angle formulae

Small angle approximations for trig

• Sin x = x

• Tan x = x

• Cos x = 1-x²/2

Double angle formula