3. (i) Differentiate y=x^3-4x^2
Answer: 3x^2-8x
(ii) Find the gradient of y= x^3-4x^2 at the point (2,-8).
Answer: -4
(iii) Find the equation of the tangent to the curve y= x^3-x^2 at the point (2,-8)
Answer: y= -4x
(iv) Find the co-ordinates of the other point at which this tangent meets the curve.
I need help with this one please! I get stuck when trying to solve he two equations for the tangent and the curve simultaneously.

Question

3. (i) Differentiate y=x^3-4x^2
Answer: 3x^2-8x
    (ii) Find the gradient of y= x^3-4x^2 at the point (2,-8).
Answer: -4
(iii) Find the equation of the tangent to the curve y= x^3-x^2 at the point (2,-8)
Answer: y= -4x
(iv) Find the co-ordinates of the other point at which this tangent meets the curve.
I need help with this one please! I get stuck when trying to solve he two equations for the tangent and the curve simultaneously.

phi · Answer

are you asking about part (iv) ?

anonymous · Answer

yes

phi · Answer

(iv) Find the co-ordinates of the other point at which this tangent meets the curve.

As this graph shows (see below), the tangent meets another point on the curve (but not as a tangent)
we have
y= -4x
y= x^3 -4x^2
and ask where they intersect:
-4x = x^3 -4x^2
x^3-4x^2 +4x = 0
x(x^2-4x+4) =0
from which we get

x=0  and (x-2)^2=0  i.e. x= 2
thus 0,0 is the other point

anonymous · Answer

Oh I see now! Thank you very much!