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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^2
Then you have to differentiate implicitly:
use product rule on xy to get:u = x v =ydu = 1 dv = dy/dx
so xy differentiates t...

The first step in solving this problem is to identify that it is an integral that needs to be solved by parts. When you see an integral, check if it is in the form uv, where u and v are both functions...