For graph of function defined by y=x^3-6x, find the coordinates of the points which the gradient is 6

I was wondering how you would do this question.

Thank You

From y = x^3 - 6x, first find the gradient function:

y' = 3x^2 - 6

Now, the gradient given is 6, so we need to find x such that:

3x^2 - 6 = 6

Solve for x:

3x^2 = 12

x^2 = 4

x = +/- 2

Now, plug these two values back into the original equation:

y = (2)^3 - 6(2) = 8 - 12 = -4
y = (-2)^3 - 6(-2) = -8 + 12 = 4

So, the two solutions are (2, -4) and (-2, 4).