Given f(x) = { x^3 - 1, x ≤ -1....(Please help)

Question

Given f(x) = { x^3 - 1 x ≤ -1

2mx^2 - 5kx + 1, -1 < x < 2,

(1 - 4x)/x + 5 x≥ 2 }

Find the values of m and k such that f is continuous.

Answer 1

In order to make f(x) continuous, just equate the equations at the borders of the intervals:

2mx^2 - kx + 1 = x^3 - 1 at x = -1 and

2mx^2 - kx + 1 = (1-4x)/5 at x = 2

This leads to linear simultaneous equations in k and m that can then be solved for k and m.

Good luck.

Strictly speaking, the middle intermal only needs to approach the correct values as a limit approaching -1 and 2.