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dy/dx = 3x^2-2x+6
At (1,5), dy/dx = 7. 7 is the gradient of the tangent, therefore the gradient of the normal at (1,5) is -1/7.
There are, mainly, three ways of doing it easily: Substitution: It consists in modifying one of the equations in such a way that x is expressed in terms of y (or y in terms of x) and then substitut...
There are a few different ways to approach this problem. The most obvious is to attempt to factorise x3 + 2x2 - 9x - 18. However it is very difficult to approach the problem like thi...
6x^2 + 7x + 2 can be written in the form ax^2 + bx + c. In order to factorise this I use the following method which can be used to factorise similar equations. Multiply 'a' and 'c' to get ac (here this is...
dy/dx = 9x^2 + 2ax + b
x = 2, dy/dx = 9(2)^2 + 2a(2) + b = 36 + 4a + b
x = 1, dy/dx = 9(1)^2 + 2a(1) + b = 9 + 2a + b
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