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Stationary points occur when f'(x) = 0. To find this, we differentiate f(x) to get f'(x) = 12x^3 - 24x^2. We know that at the stationary points are when f'(x) = 0. so we know that 12x^3 - 24x^2 = 0. We ca...

Using the Factor Theorem, we know that (2x + 1) = 2(x + 1/2) = 2(x - (-1/2) ) is a factor of p(x) if and only if p(-1/2) = 0, which is true. Now that we know a factor of ...

let f(x)=sin x f'(x) lim h-> 0 = ( sin(x+h) - sin(x))/h. f'(x) lim h-> 0 =( sin(x)cos(h) + cos(x)sin(h) - sin(x))/ h. f'(x) lim h-> 0=(sin(x)(cos(h)-1)/h + cos(x) (sin(h))/h. then as h tends to z...

Our first step should always be to make sure we understand what the question actually wants from us, in the case of most polynomial questions a rough sketch with any information we know is very useful. Fi...

There are 2 methods used for finding the gradient of a line in 2D space, depending on whether it is a straight line or a curve.
To find the gradient a straight line you must first take the equation ...