Application Of Differentiation ; Rate Of Change, Equation Of Motion , Maximum And Minimum Points And Values

Rate of Change

MAXIMUM AND MINIMUM POINTS

GENERAL EVALUATION

1. A curve is defined by f(x) = x³ -6x²-15-1 find (i) the derivative of f(x) (ii) the gradient of the curve at the point where x= 1 (iii) the minimum and maximum points
2. The distance of a particle from a starting point is S = t³ – 15t² +63t – 40 where t = time taken in seconds, find the (i) distance of the particle from the starting point when the particle is at rest

(ii) velocity when the acceleration is zero

Reading Assignment : New FURTHER MATHS PROJECT 2 page 149-167

WEEKEND ASSIGNMENT

1. Find the value of x at which the function y = x² – 7x² + 15x has the greatest value a) 5/3 b) 5/4 c) 5/2 d) 5/6
2. Find the values of  x at  the turning point of  y = 2x³ – 3x² -12x + 8  a) 1 or 2  b) -1 or -2  c) – 1 or 2 d) 1 or -2
3. Find the maximum value of the function 3x² –x³ a) 2 b) 4 c) 0 d) 6
4. Find the minimum value of the function f(x) = x³ + 3x² – 9x + 1 a) -3 b) -5 c) -4 d) 0
5. At what rate is the area of a circle changing with respect to its radius when the radius is 5cm a) 25𝜋 b 15𝜋 c) 20𝜋 d) 10𝜋

THEORY

1. The displacement of a particle is given as S = 12t – 15t² + 4t³ where t is the time taken . Find the velocity and acceleration of the particle after 3 seconds
2. Find the maximum and minimum points and values of the curve y = x³ – 6x² + 9x –