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Vera_Pavlovna [14]
3 years ago
7

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
Mathematics
1 answer:
mel-nik [20]3 years ago
8 0

Answer:

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

Step-by-step 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,

\frac{dy}{dx}=\frac{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.

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