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a) When differentiating y, the method with each term is to 'times by the power and minus 1'. In order to apply this, we need every term to consist of a coefficient multiplied by a power of x. To start wit...

Use double angle formula to rearrange for cos2x

this gives: x/2 + 1/4sin2x + C (constant)

differentiating the equation gives dy/dx = 4x^3 - 12x^2 dy/dx = 4x^2(x - 3)

at a turning point, dy/dx = 0. Solving the equation 4x^2(x - 3) = 0 yeilds x = 0, x = 3

putting 0 and 3 back into ...

a). Find stationary point: Stationary point is the point at which the gradient equals zero. So first we must find the gradient and the set it to zero and solve: dy/dx= 2x-54x^(-1/2); now we set this to ze...

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