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Suppose y is a function of x: y = f(x) At the maximum/minimum of the curve y, the first derivative of the function (with respect to x) is equal to zero:dy/dx = 0To check ...

How do I solve the following question. 'Find the values of x such that 2log₃(x) - log₃(x-2) = 2'.To simplify this equation in order to solve it, the first step is to simplify the 2lo...

The method of integration by parts is working upon the Product Rule in differentiation. We know the Product Rule to be d/dt (uv) = uv' + vu', where u and v are separate functions and u' and v' are the cor...

To solve these algebraically, we need to eliminate one of the two variables (either x or y) and solve for the remaining variable. We then substitute the answer found into one of the two given equations to...

1. Rearrange y - 3x = 13y = 3x + 13 2. Substitute into x^2 +y^2 = 25x^2 + (3x + 13)^2 = 25 3. Expand bracketx^2 +(9x^2 + 39x +39x +169) = 25 4. Form quadratic equation 10x^2 + 78x + 144 = 0 (Dividing b...