Thread: Need some help with the method

I've got an equation: 4x^3 - 24x^2 + 45 x - 23

A tangent is drawn at point P. (1,2)

dy/dx = 12x^2 - 48x +45

At f´(1) = 12 -48 + 45 = 9

2 = 9(1) +c

y = 9x - 7

Show that the x coordinate of point q is 4.

9x-7 = 4x^3 - 24x^2 + 45 x - 23

0 = 4x^3 - 24x^2 + 36 x - 16

I found x = 4 using polyrootfinder on my gdc and was wondering if there is any other way of coming to that answer?

I imagine is the point where the tangent cross the curve, doesn't it ?

Your method is good, but you can solve the equation if you notice that is solution, then put in factor..

That is correct. I see what you mean however I'm quite unfamiliar with factorisation with 3rd degree polynomials (I'm still a middle school student :S). Could you care to elaborate?

Of course !



You have to test some values such as 1, 2, 3, -1, -2, -3.

Indeed here : so we can put in factor :



which we develop :

And we identify each coefficient

After resolution we get :

Hence and you know the factorisation 2nd degree polynomials.

Is my english correct ?