Question

At What points on the graph of f(x)=18x-2x^3 is the slope equal to -6

Answer 1

slope is given by df(x)/dx = 18 - 6x^2 in this case.

slope = -6

implies,

18 - 6x^2 = -6

Therefore,

6x^2 = 24

Therefore,

x^2 = 4

Therefore, x = +sqrt(4) or - sqrt(4)

= +2 or -2

Therefore, at x = 2 and x = -2, the slope = -6