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secondary 4 | A Maths
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Will do the rest all slowly
I will do finish this one first before going on to the other one and finally the quotient rule one, in this order, provided I have time. I will do them at a slow rate.
As you proceed in this chapter, you must not forget tour earlier topics. Notice how a seemingly innocent differentiation question suddenly becomes a cubic equation in x. Fortunately, we are able to extract x out as a common term here, but not all cases we can do that.
In the event that the cubic equation requires you to guess a number, remember that x = 3 was already one of the points of intersection (obviously), so x - 3 is a factor.
I have included the quadratic curve, the tangent at A, the normal to the other point (which is parallel to the tangent at A) and the tangent to the other point (which is perpendicular to this normal at the same point).
At the last part we reject x = 3, because the tangent at x = 3 cannot be “parallel” to the tangent at x = 3.
You cannot talk about the parallelity of two “identical lines”. Parallel is meant for two lines which have the same gradient but do not meet at all.