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First, we must find the value of x that corresponds to the stationary point, i.e. where the gradient (dy/dx) is zero. This will be in terms of 'a' (if we change 'a,' we change the shape of the function by...

First draw out the free body diagram for the problem, marking on all forces acting on the objects ie. the mass of the block and the reaction force normal to the plane and the forces acting due to friction...

Setting (1 + kx)ⁿ equal to 1 - 6x + 30x² + ..., the binomial expansion can be applied to the LHS, by making use of the formula provided in the formula book. In this case, where x app...

Lets think about what stationary points actually mean. A stationary point of a curve is where the gradient is equal to 0. Illustrate by plotting the graph of y = x^3.We know that by differentiating the eq...

Let's start with differentiation. Differentiation is the instantaneous rate of change. We differentiate functions to find their rate of change as a function of their input values, this is known as a funct...