Find the coordinates of the points on the curve $y = 2x^3 - 9x^2 - 12x + 7$ where the gradient is 12

Question

I've tried multiple times so I must be doing something wrong. I differentiated to get $ dy/dx = 6x^2 - 18x - 12 $ and then I set that equal to $12$ and rearranged/factorised to get $x = 4$ and $x = -1$.

The answer is (according to the back of the book): $(-1,8)$ and $(4,-57)$.

Answer 1

You are on the right track. Once you have found the x-values ($ -1$ and $4$), plug those (separately) into the original equation and solve for the corresponding y-coordinates.

Answer 2

you must solve the equation $$f'(x)=6x^2-18x-12=12$$ for $x$

Answer 3

The question asked for the coordinates, not the x values.

You have the correct x values. Now find f(x) for each to get the coordinate pairs (x, f(x)).