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Given y=x^3-x^2+6x-1, use diffferentiation to find the gradient of the normal at (1,5).

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.
KR
2872 Views

How can a system of two linear equations be solved?

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 substitute that exp...
PA
3224 Views

x^3 + 2x^2 - 9x - 18 = (x^2 - a^2)(x + b) where a,b are integers. Work out the three linear factors of x^3 + 2x^2 - 9x - 18. (Note: x^3 indicates x cubed and x^2 indicates x squared).

There are a few different ways to approach this problem. The most obvious is to attempt to factorise x 3 + 2x 2 - 9x - 18. However it is very difficult to approach the problem like this. fortunately the ques...
CB
5102 Views

Factorise 6x^2 + 7x + 2

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 6 ...
HP
14424 Views

A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.

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 36 + 4a + b = 2(9 + 2a + b) b = 18 x = -1, dy / dx = 0 = 9(-1)^2 + 2a(-1) + 18 9 - ...
AR
3035 Views