This is the question:
A curve has the equation $y= 3x^3 – 2x^2 + 2x$. The equation of the tangent to the curve when $x=1$ is $y = 7x + 4$. Find the coordinates of the curve where the tangent meets the curve again.
I tried to substitute the equation of the tangent into the equation of the curve but I got a cubic equation that did not give any possible solutions.
The answer to this question is $\left(-\dfrac 43, -\dfrac{40}3\right)$.
Best Answer
You are wrong about the tangent line. It is $y=7(x-1)+3=7x-4$. Using this, you will get the correct answer.