Question

The graph of the function f(x) = (x + 2)(x − 4) is shown.

On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (1, negative 9), and goes through (4, 0).
Which describes all of the values for which the graph is negative and increasing?

all real values of x where x < −2
all real values of x where −2 < x < 4
all real values of x where 1 < x < 4
all real values of x where x < 0

Answer 1

We need x where f(x) < 0 and f is increasing.

f(x) = (x+2)(x−4) is negative between its roots: −2 < x < 4.
f'(x) = 2x − 2, so f is increasing when x > 1.

Intersection: 1 < x < 4.

So the correct choice is: all real values of x where 1 < x < 4.