2The volume of the container, V cm3, is given by = (8ℎ2 − 1 ℎ3) where h 3

cm is the height of the container.

(a)The container is heated up and its height increases from 4 cm to 4.1 cm. By using differentiation, find the approximate change in the volume of the

container. [3 marks]

(b)(i) Find the height of the container when the volume is maximum. [2 marks]

(ii) Hence, calculate the maximum volume of the container. Give your answer

in terms if . [2 marks]

29 mil

step-by-step explanation:

0 is its x and y coordinate

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.