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Find the coordinates of the stationary point of the graph y = 3x^2 - 12x

Firstly, we need to differentiate the equation to find an equation for the gradient of the line.dy/dx = 6x-12We know the original graph was quadratic, and therefore only has one stationary point. This is whe...
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Answered by Jack M. • Maths tutor
6928 Views

I struggle to simplify the following equation: (see answer)

3l 2 mn + nl 2 m - 5mn 2 l + l 2 nm + 2n 2 ml - mn 2 The first step is to ask yourself if there is anything that could help you simplify the equation, any recurring term or common factor. Here, we note that ...
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Answered by Luc S. • Maths tutor
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Integral of Cosec(x)/Sec(x) (i.e. Use of trignometric identities)

∫ Cosec (x)/Sec (x) dx∫ [1/Sin (x)]/ [1/Cos (x)] dx∫ [1/Sin (x)] * [Cos (x)] dx∫ Cot (x)= ln [Sin (x)] + c
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Answered by Sean M. • Maths tutor
8053 Views

Two numbers add to make 1000. What would they have to be to maximise their product?

We can write the two numbers as x and 1000-x, because x+(1000-x) = 1000 for any x we pick. Now we want to maximise the product x(1000-x); expanding the brackets gives us 1000x-x 2 which is easier to work wit...
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Answered by Ankur D. • Maths tutor
6860 Views

Find the derivative of sin^2(x)

Using the chain rule we differentiate the ‘outside function’, then differentiate the ‘inside function’ and multiply both derivatives together giving 2sin(x)cos(x)
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Answered by David R. • Maths tutor
5286 Views