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Differentiation is a very useful concept; informally it tells us how 'fast' something is changing. A real-life example is given by the first and second derivatives of distance with respect to time: the fi...

To calculate the minimum value of A we first need to establish an equation for A. The surface area of a cuboid is relatively simple to figure out we simply work out the area of the faces and sum them toge...

First we find two numbers that that add up to -8 and multiply to make 15. In this case the numbers are -3 and -5. This means we can now factorise the quadratic to give (x - 5) (x - 3) = 0. For the above t...

y=-4x-1
(-4x-1)^2 +5x^2 +2x=0

16x^2 +8x +1 +5x^2 +2x=0

21x^2 +10x + 1 =0
(7x+1)(3x+1)=0

x=-1/7 or -1/3

y= -3/7 or 1/3

Firstly find the gradient of A, through differentiation: dy/dy = 3x² – 2x + 1. To find the gradient at P, substitute the x value of the P coordinate into this equation: dy/dx = 3(2)²...