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df/dx = 4x - 2
turning point when differential = 0
==>
4x = 2 hence; x = 0.5
When x = 0.5 f(x) is equal to (substitute) 3.5
hence the turning point is at (0.5,3.5)<...
By looking at both equations you spot that the 'x' in the first equation has coefficient equal to 1, so it would be quite convenient to make 'x' the subject of the first equation and then substitute what ...
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...
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