Find Increasing Intervals: Analyzing y = (x+6)(x-8)

Find the intervals where the function is increasing:

y=(x+6)(x8) y=(x+6)(x-8)

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the intervals where the function is increasing:

y=(x+6)(x8) y=(x+6)(x-8)

2

Step-by-step solution

To find the intervals on which the quadratic function y=(x+6)(x8) y = (x+6)(x-8) is increasing, we perform the following steps:

Step 1: Expand the quadratic to standard form:
y=(x+6)(x8)=x22x48 y = (x+6)(x-8) = x^2 - 2x - 48

Step 2: Find the derivative of the function:
The derivative, f(x) f'(x) , is found by differentiating x22x48 x^2 - 2x - 48 :
f(x)=2x2 f'(x) = 2x - 2

Step 3: Determine where the derivative is positive:
Set f(x)>0 f'(x) > 0 :
2x2>0 2x - 2 > 0

Solve for x x :
2x>2 2x > 2
x>1 x > 1

Therefore, the function y=(x+6)(x8) y = (x+6)(x-8) is increasing on the interval x>1 x > 1 .

Thus, the correct answer is x>1 x > 1 .

3

Final Answer

x>1 x>1

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:

XXXAAA

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations