Question

The graph of the function f(x) = (x – 4)(x + 1) is shown below.

On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0).

Which statement about the function is true?

The function is increasing for all real values of x where
x < 0.
The function is increasing for all real values of x where
x < –1 and where x > 4.
The function is decreasing for all real values of x where
–1 < x < 4.
The function is decreasing for all real values of x where
x < 1.5.

Answer 1

The last statement is true.

Reason: f(x) = x^2 − 3x − 4 has derivative f'(x) = 2x − 3, which is negative when x < 3/2 = 1.5. So the parabola is decreasing for all x < 1.5 (and increasing for x > 1.5).