Differentiation

Gradient function

After studying this section you should be able to:

  • use differentiation to find the exact value of the gradient of a curve
  • find the equation of the tangent and normal to a curve at a given point
  • determine whether a function is increasing or decreasing in an interval
  •  locate turning points and use the second derivative to distinguish between them

Gradient function

  • In AQA Core 1, n will be a positive integer.
  • Differentiate each term separately.
  • Remember that x0 =1.
  • When you differentiate a constant, the result is zero.
  • You cannot differentiate a product term by term.
  • You cannot differentiate a quotient term by term.

Tangents and normals

  • The normal at a point is perpendicular to the tangent.

Curve sketching

  • The first two types of stationary point are also known as turning points.

The second derivative

PROGRESS CHECK

Category
Geometry
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