Question

If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (2, 12).

Answer 1

k = 1

Explanation:

since the graph contains the point (2, 12 ) then the coordinates of the point make the equation true.

substitute x = 2 and f(x) = 12 into the equation and solve for k

12 = k(2)³ + 2² - k(2) + 2 , that is

12 = 8k + 4 - 2k + 2

12 = 6k + 6 ( subtract 6 from both sides )

6 = 6k ( divide both sides by 6 )

1 = k