Podcast
Questions and Answers
What is the equation of the function for which we are finding the tangent slope?
What is the equation of the function for which we are finding the tangent slope?
What is the required slope of the tangent line to the function at specific points?
What is the required slope of the tangent line to the function at specific points?
Which of the following points is NOT a solution for the tangent line slope of 1/5?
Which of the following points is NOT a solution for the tangent line slope of 1/5?
What conclusion can be made about the number of points where the slope of the tangent line is 1/5?
What conclusion can be made about the number of points where the slope of the tangent line is 1/5?
Signup and view all the answers
Which of the following pairs correctly represent the coordinates at which the tangent has a slope of 1/5?
Which of the following pairs correctly represent the coordinates at which the tangent has a slope of 1/5?
Signup and view all the answers
What value of x results in the function f(x) = x^2 + 5 yielding a slope of 1/5 for its tangent line?
What value of x results in the function f(x) = x^2 + 5 yielding a slope of 1/5 for its tangent line?
Signup and view all the answers
Which of the following pairs represents a point on the graph where the tangent slope is 1/5?
Which of the following pairs represents a point on the graph where the tangent slope is 1/5?
Signup and view all the answers
Which statement accurately reflects the existence of tangent points with a slope of 1/5?
Which statement accurately reflects the existence of tangent points with a slope of 1/5?
Signup and view all the answers
At which of the following points is the function f(x) = x^2 + 5 likely to have a slope of 1/5?
At which of the following points is the function f(x) = x^2 + 5 likely to have a slope of 1/5?
Signup and view all the answers
Which of the following options implies that there are no valid coordinates for the tangent slope of 1/5?
Which of the following options implies that there are no valid coordinates for the tangent slope of 1/5?
Signup and view all the answers
Study Notes
Finding Tangent Line Slope Points
- The function is f(x) = x / (x + 5)
- The slope of the tangent line to f(x) at a given point is equal to the derivative of f(x) at that point.
- The problem asks for the x-values where the derivative (slope) is equal to 1/5.
- The correct answer is C. (0, 0) and (-10, 2).
Finding the Derivative (Slope)
- Calculating the derivative of f(x) using the quotient rule: f'(x) = [(x + 5)(1) - (x)(1)] / (x + 5)² f'(x) = 5 / (x + 5)²
Setting the Derivative Equal to 1/5
- Setting f'(x) = 1/5: 5 / (x + 5)² = 1/5
Solving for x
- Cross-multiplying to solve for x: 25 = x² + 10x + 25 x² + 10x = 0 x(x + 10) = 0 Solutions are x = 0 and x = -10
Finding Corresponding y-values
- Substitute x = 0 into the original function to find the corresponding y-value: f(0) = 0/(0 + 5) = 0. This gives coordinate (0, 0)
- Substitute x = -10 into the original function to find the corresponding y-value: f(-10) = (-10)/(-10 + 5) = (-10)/(-5) = 2. This gives coordinate (-10, 2)
Conclusion
- The points where the tangent line has a slope of 1/5 are (0, 0) and (-10, 2).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the concepts involved in finding the slope of tangent lines for the function f(x) = x / (x + 5). You will learn to calculate the derivative using the quotient rule and find the x-values where the slope equals 1/5. Additionally, you'll discover how to determine the corresponding y-values for these points.
