Question

A coordinate axis is drawn with a parabola pointing up that has vertex of 0,3. Determine the intervals on which the function is increasing, decreasing, and constant. Increasing x < 0; Decreasing x > 0 Increasing x > 0; Decreasing x < 0 Increasing x < 3; Decreasing x > 3 Increasing x > 3; Decreasing x < 3

Answer 1

Option (2). Increasing x > 0; decreasing x < 0

Explanation:

Equation of the parabola having vertex (0, 3) will be,

y = (x - 0)² + 3

y = x² + 3

To check the function is increasing or decreasing in the given intervals we will find the derivative of the function,

`(dy)/(dx)=(d)/(dx)(x^(2)+3)`

y' = 2x

For x < 0 Or x = -1

y' = 2(-1)

= -2 < 0

Therefore, function is decreasing in x < 0

For x > 0 Or x = 1

y' = 2(1) + 3

= 5 > 0

Therefore, function is increasing in x > 0

Option (2) is the answer.