Find Intervals of Increase and Decrease: y = (x - 4.4)(x - 2.3)

Find the intervals of increase and decrease of the function:

y=(x4.4)(x2.3) y=\left(x-4.4\right)\left(x-2.3\right)

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1

Understand the problem

Find the intervals of increase and decrease of the function:

y=(x4.4)(x2.3) y=\left(x-4.4\right)\left(x-2.3\right)

2

Step-by-step solution

Let's solve the problem step by step:

  • **Step 1:** Identify the points p p and q q from the function y=(x4.4)(x2.3) y = (x-4.4)(x-2.3) . Here, p=4.4 p = 4.4 and q=2.3 q = 2.3 .
  • **Step 2:** Calculate the vertex x x -coordinate using the formula for the midpoint: x=p+q2=4.4+2.32 x = \frac{p+q}{2} = \frac{4.4 + 2.3}{2} .
  • **Step 3:** Compute the value: x=6.72=3.35 x = \frac{6.7}{2} = 3.35 .
  • **Step 4:** Since the quadratic has a positive leading coefficient after expansion (implying it opens upwards), the function decreases on (,3.35) (-\infty, 3.35) and increases on (3.35,) (3.35, \infty) .

Therefore, the function is decreasing for x<3.35 x < 3.35 and increasing for x>3.35 x > 3.35 .

The correct choice that matches this conclusion is:
:x<3.35:x>3.35 \searrow: x < 3.35 \\\nearrow: x > 3.35

3

Final Answer

:x<3.35:x>3.35 \searrow:x<3.35\\\nearrow:x>3.35

Practice Quiz

Test your knowledge with interactive questions

Note that the graph of the function shown below does not intersect the x-axis

The parabola's vertex is A

Identify the interval where the function is decreasing:

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