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First we add up all the 'x' terms. So the equation 7 - 4x = x + 8 becomes 7 - 4x - x = x +8 - x  => 7 - 5x = 8. Now we can do the same with the ot...

First, expand (x-2)²:

= (x-2)(x-2),

= x² - 2x - 2x + 4

= x² - 4x + 4

Add on the +7:

= x² - 4x + 11

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As we know, to find a gradient in a linear function, we have to calculate the difference in the objective function (usually y) by the difference in the choice variable (commonly x), you may know this as r...

Integrating by parts is simple. Simply put the equation into two parts, U and dV/dx. When considering which part of the original function will be U and which part will take dV/dx, you should consider whic...