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Firstly remember that each part of the equation can be differentiated separately. Let's label each part:

Part A: 2(x^2)y

Part B: 2x

Part C: 4y

Part D: -cos(piy)

Part E: ...

= (30/15+11/15) - (3/3+1/3) = (41/15)-(4/3) = (41/15)-(20/15) = (21/15) = (7/5)

There will be intersection when x^2 + 4x + 3 = kx + 2. Our goal is to find the values of k which would only give one solution to this quadratic equation, which would make the lines 'tangent' to each other...

2x²(x² + 2 - 16x)

First, convert the units so you can compare more easily. 

0.72m = 72cm = 720mm

So 1 shelf is 720mm and 1 textbook is 30mm wide. 

To find the maximum number of books that can be stored...