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AS Core 1 For Edexcel - Pearson
Chapter 7: Graphs of function
to answer this question we first differentiate y=3x^2-4x-4 getting the gradient function 6x -4.
a= gradient function so y= (6x-4)(x) +1
expand and we get y=6x^2-4x+1
next we need to find the coordinates of where the curve and the tangent meet so we do this.
6x^2 -4x +1=3x^2 -4x +1 which is = 3x^2 -3
expand to find x (3x-3)(x+1) so x is equal to 1 or -1
substitute them both into y= 3x^2 -4x +4 and we get y= 3 or 11
so our coordinates when both lines meet is (1,3) and (-1,11)
and if we substitute them into are tangent line (y=ax+1) then we can find the value for a
3=a+1 and 11= -a+1 so a = 2 or -10
(I tend to make mistakes so be critical and point it out if i have)
either way hope this helps!