Answer:
x ∈ {-2, 6}
Step-by-step explanation:
You want the solutions to ...
f'(x) = 2
Taking the derivative, you get ...
f'(x) = 3x^2 -12x -34 = 2
Subtract 2 and factor:
3x^2 -12x -36 = 0 = 3(x^2 -4x -12) = 3(x -6)(x +2)
The values of x that satisfy this equation are the values of x that make the factors be zero: x = 6, x = -2.
The slope of a tangent to the curve will be 2 at x=-2 and at x=6.
