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y=mx+c where m is the gradient and c is the y-intersect hence gradient=6 and y-intersect = 2 . this can also be found by differentiating the equations dy/dx = 6 and setting x=0 to find the y value.

You're right that x = 4 is a solution to the equation - but the problem is it's not the only solution, x = -4 also works.You have to be careful not to take a shortcut by simply taking the square root of b...

Notice that this is a quadratic. First you should try factorisation, then if unsuccessful try completing the square (or the quadratic formula). In this example, factorisation is not possible (I can this f...

Using integration by parts split it into v'=(1/x^3) and u=ln(x). v=-1/2x^2 and u'=1/x. Integral ln(x)/(x^3) = u*v - Integral u'*v = -ln(x)*1/2x^2 - 1/4x^2 + c

In order to integrate the expression we must first rewrite it in terms of Partial Fractions i.e. A/x and B/(2-x), so that when multiplied together we have a fraction with same denominator as the expressio...