Question

Use the table to describe the intervals over which f(x) = 15x² is increasing and decreasing.

f(x)=15x²
(x,y)
(-2,60)
60
15
(-1,15)
0
15
60
X
-2
-1
0
1
2
(0,0)
(1,15)
(2,60)
The function f(x) is increasing over the interval x>0¹.
(Simplify your answer. Type an inequality.)
The function f(x) is decreasing over the interval
(Simplify your answer. Type an inequality.)

Answer 1

Explanation:

The function f(x) = 15x² is increasing over the interval x > 0.

To see why, we can look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. When x is zero, f(x) reaches its minimum value of zero. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is increasing over the interval x > 0.

The function f(x) is decreasing over the interval x < 0.

To see why, we can again look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. But as x approaches zero from the left, f(x) begins to decrease, reaching its minimum value of zero at x = 0. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is decreasing over the interval x < 0.