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the curve crosses the graph at the x axis at 0.5,3 and -4 so f(0.5)=0, f(3)=0,f(-4)=0. All linear factors are the form of g(x)=(x-a) so 0=g(0.5)=0.5-a. rearranging we get that a=0.5 ie g(x)=x-0.5 similarl...
Factorise denominator using the factor theorem giving - 1/(x+1)(x+2)(x-1) Use partial fractions to turn this into an easier form to integrate giving - 1/3(x+2) + 1/6(x-1) - 1/2(x+...
Firstly notice that the coordinates of the points where the tangent to the curve is parallel to the x-axis are precisely the points where the rate of change of y with respect to x is not changing. That is...
logF=logG+logH−log(1/M)−2*logR Simplify RHS using law of logarithms,
logF=log(GH)−log(1/M)−2logR using law of addition logF=log(GHM)−2logR ...
This question requires differentiating the equation to find where its gradient is equal to zero. Differentation is done via a simple equation --> if y = xn then dy/dx = nxn-1
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