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We know that A+B = 8 so we should first count the number of ways that the two dice could total 8. (A = 2, B = 6), (A=3, B=5), (A=4, B=4), (A=5, B=3) , (A=6, B= 2) -- this gives 5 possible waysWe also know...

To find the turning point of the equation, it should be recognised that we desire the point at which the gradient is 0. The gradient is given by dy/dx and hence we differentiate the equation with respect ...

y=2x(x²-1)⁵ --> y=uv, where u=2x; v=(x²-1)⁵ --> thus product rule required.u'=2v'=10x(x²-1)⁴Product rule: dy/dx = uv' + v'uTherefore...

Starting by factorising the curve equations: the first one factorises to y = (x-3)(x-2) and the second one becomes y=(2-x)(2+x). From this, a rough sketch of the curves can be drawn and it can be seen tha...

We can differentiate the expression using the quotient rule. If f(x)=u(x)/v(x) then f'(x)=(u'(x)v(x)-u(x)v'(x))/v(x)^2. In this case u(x)=3x^2-5x so u'(x)=6x-5 and v(x)=4x^3+2x^2 so v'(x)= 12x^2+4...