Search over 10,000 free study notes

This fact can be deduced several ways, and I would encourage tutees to find other methods, (such as using implicit differentiation, or the chain rule.) However one of the simplest explanations is given below...

y=2x 3 - ax 2 + 8x +2. If we are told that B is the stationary point of the curve, then it is at that point where the gradient of the curve is equal to 0. In order to find the gradient of the curve at this p...

8(1-sin^2(x))+6sin(x)-6=38(1-sin^2(x))+6sin(x)-9=08sin^2(x)-6sin(x)+1=0(2sin(x)-1)(4sin(x)-1)=02sin(x)-1=0 4sin(x)-1=02sin(x)=1 4sin(x)=1sin(x)=1/2 sin(x)=1/4x=(pi)/6 , 5(pi)/6 , 0.253 , 2.89

1st we will log both sides of the equation7 (x+1) = 3 (x+2) becomes log7 (x+1) = log3 (x+2) NEXT we will use the power law which is log a (x) k =k log a (x)This turns log7 (x+1) = log3 (x+2) to (x+1) log7 = ...

Recognise that the form this question is a circleRemember alternate circle equation (x + a) 2 + (x + b) 2 = r 2 Where centre of circle (-a,-b) and r is the radiusTo get the right form use complete the square...