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To find the coordinates of the point, we have to solve the equations simultaneously. To do this, we need the same number for the coefficient of x or y in each equation. Arbitrarily, we will chose to match...

First we will differentiate y to find dy/dx= 4x³-16x. Stationary points exist at dy/dx=0 so we set 4x³-16x=0 and solve for x. x(4x²-16)=0. So x=0 or 4x²-16=0. I...

First remember that a parametric curve z = (x(t), y(t)) can be differentiated using the following formula (derived using the chain rule): dz/dt = (dy/dt)/(dx/dt). We should now find dy/dt and dx/dt (which...

I have written "… " where I would imagine the student is replying. I have then provided prompts assuming that the student did not come up with the answer straight away. Integration can ...

We are trying to solve 27^-2/3. Firstly, using the index rule a^xy= (a^x)^y, this can be rewritten as (27^1/3)^-2. Lets tackle the value inside ...