Question

Consider the function :

f(x)=2x^2+4x−6. Is the function increasing or decreasing over the interval [-3, -1)?
A. increasing.
B. decreasing.

Answer 1

The function f(x) = 2x^2 + 4x - 6 is increasing over the interval [-3, -1).

Step-by-step explanation:

The function f(x) = 2x^2 + 4x - 6 represents a quadratic function. In order to determine whether the function is increasing or decreasing over the interval [-3, -1), we need to analyze the sign of the derivative of the function for values within that interval.

To do this, we take the derivative of the function f(x) to find:

f'(x) = 4x + 4.

Next, we evaluate the derivative at different values within the given interval:

f'(-3) = -8, f'(-2) = -4, and f'(-1) = 0.

Since the derivative changes from negative to positive as we move from -2 to -1, we can conclude that the function is increasing over the interval [-3, -1).