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Differentiate wrt x. This leaves dy/dx = 3x^2 + 6x and equate this to 0 as we are looking for stationary points.So, 3x^2 + 6x = 0. Factorise to get x(3x +6) = 0. So x = 0 and x = -2 are the two solutions....

Re-arrange y-2x-4=0 to y=2x+4Substitute y=2x+4 into 4x^2+y^2+20x=0 to get 4x^2+(2x+4)^2+20x=0Expand the brackets to get 4x^2+(4x^2+16x+16)+20x=0Simplify to get 8x^2+36x+16=0Divide by 4 to get 2x^2+9x+4=0F...

expand the brackets to obtain x^2=4(x^2-6x+9)expand the brackets to obtain x^2=4x^2-24x+36rearrange to obtain 0=3x^2-24x+36factorise to obtain 0=(3x-6)(x-6)solve for x=6 or x=2

The curve is a quadratic equation because it has a x^2 - as it is positive it will be a u shaped parabola. The equation can be factorised by thinking of two numbers which add to make 4 (the b value) and m...

Chain rule:when we have a function on its own raised to a certain power. eg: f(x)=(2x+3)³--> f'(x)=3*2(2x+3)²
Product rule:<...