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(a) The curve is defined by y=(2x-3)^5. To find x=w when y=-32, we must substitute these values into the equation C and re-arrange to find w. -32=(2w-3)^5. First we must remove the power of 5 by doing pow...
This is a standard question that may be found in a C4 mathematics paper. Students should use knowledge of the volume of revolution formula V = piint_{a}^{b} y2dx to find the expression V =...
To begin, we must first use the fact that turning points of a graph occur at points where the gradient is equal to zero, in other words, points where dy/dx =0. Differentiating the equation with and settin...
This questions is a proof type question, which means that you need to get to a specific formula. Usually, these questions give you clues in order to prove it. In this case it tells you that the equation h...
Expand to get xy+3y-4x-12=x^2+y^2Rearrange to xy+3y-4x-12-x^2-y^2Then you have to differentiate implicitly:use product rule on xy to get:u = x v =ydu = 1 dv = dy/dxso xy differentiates t...
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