The diagram shows an open water container in the shape of a triangular prism of length y cm.
The vertical cross-section is an isosceles triangle with sides 5xcm, 5xcm and 6xcm.
The water container is made from 500 cm2 of sheet metal and has a volume of V cm³.

a. Express y in terms of x.

b. Show that 

c. Find the value of x for which V has a stationary value.

d. Show that the value in part c is a maximum value.

Transcribed Image Text:

V = 600x - 144 5 x³.