Specific Objectives

By the end of this topic, the learner should be able to:

(a)    Find average rates of change and instantaneous rates of change

(b)   Find the gradient of a curve at a point using tangent

(c)    Relate the delta notation to rates of change;

(d)   Find the gradient function of a function of the form  (n is a positive integer)

(e)    Define

(i)                 Derivative of a function

(ii)               Derived function of a polynomial

(iii)             Differentiation

(f)    Determine the derivative of a polynomial

(g)   Find equations of tangents and normals to the curves

(h)   Sketch a curve

(i)     Apply differentiation in calculating distance, velocity and acceleration

(j)     Apply differentiation in finding maxima and minima of a function.