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There are two ways to prove they intercept (you can choose whichever one you prefer). Say we have two straight lines, for example: r₁ = 3i + 4...

Here we have a product of two functions - they are being multiplied together - so we need to use the product rule. The product rule is: if y = u·v, dy/dx = v·u' + u·v' (where f' stands for df/dx). u = x^4...

Firstly we must take the 2 out of the bracket, as a binomial expansion must have a coefficent of 1

(2 + x) ⁵  = 2⁵ (1 + 0.5x) ⁵

Then, it is a good idea to qu...

Stationary points occur when the gradient of the function is zero. They can be visualised on a graph as hills (maximum points), as troughs (minimum points), or as points of inflection. (I would draw all t...

This a relatively simple question which requires the use of the chain rule to solve. First we set u = sin(x)  so we then have y = u² . Next we perform do differentiations, one on u as a functio...