ABSTRACT
At the end of this chapter, you should be able to:
• determine rates of change using differentiation • solve velocity and acceleration problems • understand turning points • determine the turning points on a curve and determine their nature • solve practical problems involving maximum and minimum values • determine points of inflexion on a curve • determine tangents and normals to a curve • determine small changes in functions
If a quantity y depends on and varies with a quantity x then the rate of change of y with respect to x is
dy dx
Thus, for example, the rate of change of pressure p with height h is
dp dh
A rate of change with respect to time is usually just called ‘the rate of change’, the ‘with respect to time’
being assumed. Thus, for example, a rate of change of current, i , is
di dt
and a rate of change of temperature, θ ,
is dθ dt
, and so on.
