Search over 10,000 free study notes

A minimum point will have a gradient of 0 (although so will a maximum point or a point of inflection). dy/dx = 3x 2 -6x. We can substitute x = 2 into this equation to give 0 (alternatively solve 3x 2 -6x = 0...

To find the gradient of the tangent, we can differentiate to give dy/dx=3x^2+9. We can now put in x=2 to find the gradient at (2,1): 3(2)^2+9=21. Therefore the gradient is 21 at (2,1).

Firstly you should expand the brackets in this situation in order to collect the like terms, so get all the x's on one side and all the constants on the other side of the inequality. Expanding the bracket yo...

We will you use Pascal's triangle in order to find coefficients: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 so, our coefficients will be 1,4,6,4,1 now, let's expand: (2x+3) 4 =(2x) 4 +4*(2x) 3 3+6 (2x) 2 3 2 +4 (2x)*3 3 ...

For example, A(6/5, 19/5), B(2, 9/5), C(5, 3). Show that the line segments AB and BC are perpendicular. Before we begin the question, it is a good idea to remind ourselves of the definition of two lines bein...