Question

Consider functions fand g.

f(x) = x³ +5x²-x
X -2 -1 0 1 2 3
g(x) 48
Which statement is true about these functions?
6 2 -16 -84
OA. Over the interval [-2, 2], function fis increasing at the same rate
that function g is decreasing.
B. Over the interval [-2, 2], function fis decreasing at a faster rate
than function g is increasing.
OC. Over the interval [-2, 2], function fis increasing at a faster rate
than function g is decreasing.
D. Over the interval [-2, 2], function fand function g are decreasing at
the same rate.

Answer 1

To determine the rates of change of functions f and g over the interval [-2, 2], we can compare the values of the functions at the endpoints of the interval.

For f(x), we have:

f(-2) = (-2)³ + 5(-2)² - (-2) = -6

f(2) = 2³ + 5(2)² - 2 = 34

So over the interval [-2, 2], f(x) increases by 40.

For g(x), we have:

g(x) = 48 for all x

So over the interval [-2, 2], g(x) does not change.

Therefore, we can conclude that over the interval [-2, 2], function f is increasing at a faster rate than function g is decreasing.

The correct answer is (C).