Question

If g is the function given by g (x) = ⅓x³+3/2x²-70x+5, on which of the following intervals is g decreasing?

Α) (-∞, - 10) and (7, ∞)
B) (-∞, -7) and (10, ∞)
C) (-∞, 10)
D) (-10,7)
E) (-7,10)​

Answer 1

Answer: D) (-10,7)

Explanation:

First, we will graph the equation so we can have a visual.

See attached.

Next, decreasing means that the y value is decreasing as the x increases. In other words, the graph "is moving" down as it moves right.

In the graph, you can see I have highlighted this area of decrease.

The graph is decreasing between x = -10 and x = 7. We write this in interval notation as (-10,7).

D) (-10,7)