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dy/dx=12x^2+6 d^2y/dx^2=24x

When finding the equation of a straight line there are two important figures to calculate. The first being the gradient (the slope of the line) and the second being the y intercept (where the line crosses...

Just as a note before I start, some of the symbols I use here will be horribly confused, this won't be an issue with a whiteboard but doing maths in a text editor is not great so I've had to make do.

Answer = (3,17.5) maximum (4,17.33) minimum

First differentiate y = x^3/3 - 7x^2/2 + 12x + 4 to find dy/dx. Now, at turning points dy/dx = 0 and factorise to find x when dy/dx = 0. Put x back into ...

Solve via Integration by parts:

let u=2x and dv/dx=e^x

the function that is u and the one that is dv/dx is given by LATHE (easier to explain on whiteboard)

make the table: u...