SS2 FURTHER MATHS SECOND TERM
(a) Application of Differentiation
(b) Differentiation of Implicit Functions.
SUB TOPIC: APPLICATION OF DIFFERENTIATION
- Suppose an object is dropped from rest from a given height, the distance s through which the object has dropped after t seconds (ignoring air resistance) is given by the formula
- Let p(t) denote the population of a colony of bacteria after t hours. If how fast is the population growing after 3hours?
- We want the instantaneous rate of growth of growth of the population when t = 3hours.
- The distance (d metres) fallen by a stone in t seconds is given by the equation
- Find the maximum and minimum points of the curve and sketch the curve.
SUB TOPIC: IMPLICIT DIFFERENTIATION
Functions which have their derivatives in terms of it may be possible to separate completely from to different side. Such functions are called implicit function.
Examples are 22
- If 3233 find
- If 4342 find
Differentiating both side with respect to
Differentiate the following:
- Given that
- A ball rolls down an inclined plane. It travels s centimeters in t seconds and (i) how far has the ball travelled in the first second? (ii) what is its speed at the end of the fourth second?
- A particle moves along a straight so that after a time t seconds, its distance Scm from the starting point O is given by find: (a) the distances from O when the particle is momentarily at rest; (b) the velocity when the acceleration is zero.
- Differentiate with respect to x:
- Find from first principle, the derivative, with respect to x of the function
- If calculate the average rate of change(gradient) of y, w.r.t x, in the interval between x = c and x = c + h. hence find . Also find the maximum and minimum points of the curve defined by and sketch the curve.
- FIRST PRINCIPLE
- WITH RESPECT TO
- RATE OF CHANGE
- HIGHER DERIVATIVE