Question

Heinz has a list of possible functions. Pick one of the g(x) functions below, show how to find the zeros, and then describe to Heinz the other key features of g(x).. . g(x) = x^3 – x^2 – 4x + 4. g(x) = x^3 + 2x^2 – 9x – 18. g(x) = x3 – 3x^2 – 4x + 12. g(x) = x^3 + 2x^2 – 25x – 50. g(x) = 2x^3 + 14x^2 – 2x – 14

Answer 1

g(x) = x3 – x2 – 4x + 4

You can find the zeroes by factoring the equation. x2 (x - 1) - 4(x - 1) = 0

(x2 - 4) (x - 1) = 0

(x + 2) (x - 2) (x - 1) = 0

x = 2, -2, and 1

The following are the key features of g(x):

g'(x) yields the slope

g''(x) yields the concavity

g'(x) = 0 provides the critical points

g''(x) = 0 provides the point of inflection