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This question is asking us to work our way back and find the original number. We can refer to this number as 'x'. If we multiply x by 3 we get 3x. The next step is to subtract 5, so our equation now is 3x...

To factorise this equation we want to get 2 brackets. We are looking for 2 numbers which multiply to make -12 and add to make -1. So, let's see some factors of -12: -12 = (-1) x 12; (-2) x 6; (-3) x 4; (-...

First we use the product rule, so we multiply x by the derivative of (x+3)⁵. To find the derivative of (x+3)⁵ we use the chain rule. So we have 5(x+3)⁴. So the first part...

In order to solve these simultaneous equations we first want to eliminate one of the variables (x or y) and find a solution to the variable remaining (y or x) and then use this solution to find the second...

Find roots, stationary points, classify, sketch.