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The stationary point on the curve is the point on the curve where the gradient is 0. In other words the tangent to the curve at that point is horizontal. The gradient of the curve can be expressed as dy/d...

Route 1 (Standard): 1. 3x + y = -4 / 2. 3x - 4y = 6 / MINUS 2 FROM 1 / y - (-4y) = 5y / -4 - 6 = - 10 / 5y = - 10 / y = -2 /PUT y-VALUE BACK INTO ORIGINAL EQ  / 3x - 2 = -4 / 3x = ...

First, we want to convert the equation to a simpler form involving just one function of x. Squared trigonometric functions are normally good candidates for simplification, thanks to the trigonometric iden...

Answer: sin^3(x)/3 + c
The student can either solve by inspection by noticing that the derivative of sin^3(x)=3sin^2(x)cos(x).
OR
The student can use the longer method of integration by par...

When solving equations like this, the most important thing to remember is that you must do the same thing to both sides. First multiply out the brackets, multiplying the x and the 4 by 2, giving 2x+8=x+10...