Differentiation overview year 12 - created from Mind Map

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Finding the gradient function at any point x (gradient of the tangent)

Basic e.g. dy/dx

Modelling

Finding stationary points

Finding equations of tangents and normals

Nature

Max f"(x)<0

Min f"(x) > 0

Inflexion f"(x) = 0

Require point (coordinate) and gradient

tangent gradient = f'(x)

Normal gradient = -1/f'(x)

y-y1 = m(x - x1)

Optimisation problems -use volume and surface area of common solids e.g. prisms, spheres

usually substitute one formula into another

Find maximum /minimum by first differentiating and finding x values for which the stationary point occurs

Substitute x value into original formula for quantity of interest to find its min/max value

Justify the max/min using second derivative