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f(c) means let x=c. Remember that c is just an unknown number.

The expression f(c)=9 means that when we put c through the function f(x)=7-4x, it gives the answer 9. Therefore we know 7-4c...

Firstly, we calculate the y-value when x=1, namely y=e. Then we need to find the gradient of this curve at x=1, which can be determined by taking the derivative of y and then valuate it at x=1. So dy/d...

There are two ways in which this we can do this,

The first is explanding the brackets to get 1+2x+x² and differentiating to get 2+2x.

The second way is using the ...

The easiest way to solve simultaneous equations is to label the equations so you clearly follow them throughout.

For example, say you are asked to solve the unknowns for the simultaneous ...

The product rule is used when finding the derivative of the product of two functions - two functions multipled together.

If y = f(x)g(x), then

dy/dx = f'(x)g(x) + f(x)g'(x)<...