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Let y = f(x). The gradient of the tangent to the curve at a stationary point is equal to 0. To find an equation for the gradient of the curve, differentiate f(x) to get dy/dx. Because we are looking for s...

Differentiation is how to find the gradient of a line. For example, the line y = 3x has a gradient of 3. Similarly, y = 4x + 2 has a gradient of 4. However, for most lines, the gradient isn't the same alo...

This question requires an understanding of implicit differentiation, a specific form of the chain rule for derivatives.
(Aside/reminder) - Implicit function vs Explicit function:

We differentiate here to find the gradient, dy/dx, i.e. the differenitial of y in terms of x. As the right handside is purely dependant on x, this is simple. We can just multiply through by the power, i.e...

For a curve where y = f(x) the gradient of the curve is the derivative of this equation dy/dx. Stationary points of a curve occur when the gradient of the curve is zero. Hence find the expression for dy/d...