Graphing and Finding Tangent Lines of Quadratic Functions - Derivatives Help

In summary, Paul is asking for help with a problem involving graphing two parabolas and finding the equations of the tangent lines. He has already graphed the parabolas and found the derivatives, but is unsure if he is doing it correctly. He is seeking assistance with the problem.
  • #1
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I was having some trouble with a problem. The problem reads:
Sketch the graphs of y = x^2 and y = -x^2+6x-5, and sketch the two lines that are tangent to both graphs. Find equations of these lines.

I've graphed the two parabolas and drew the tangent lines. I've found the derivatives of each equation as well. I relabeled the points where the tangent line is tangent on each of the parabolas using Xsub1 and Xsub2. Am I going about doing this the correct way? Can someone give me a little help, thanks.

-Paul
 

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  • #2
What you are saying you are doing is correct. Since haven't actuall shown what you did, I can't say whether you are doing it correctly.
 
  • #3
anyone can help me with that problem ? i dunt know how to do it !
 

1. What are derivatives?

Derivatives are a mathematical concept that represents the rate of change or slope of a function at a specific point. It is calculated by finding the limit of the difference quotient as the change in the independent variable approaches zero.

2. How do you find the derivative of a function?

The derivative of a function can be found by using the power rule, product rule, quotient rule, or chain rule. These are different methods for finding the derivative of a function depending on its form. Additionally, the derivative of a function can also be found graphically by finding the slope of the tangent line at a specific point on the graph.

3. What is the relationship between derivatives and graphs?

The derivative of a function can be represented graphically as the slope of the tangent line at any given point on the graph. This means that the graph of a function and its derivative are closely related and can provide information about each other.

4. Why are derivatives important?

Derivatives are important in many fields, such as physics, economics, and engineering, because they represent the rate of change of a function. This allows us to analyze how variables are changing over time and make predictions about their future behavior.

5. How are derivatives used in real life?

Derivatives have many real-life applications, such as calculating the velocity and acceleration of moving objects, finding the optimal solutions in business and economics, and predicting the growth and decay of populations. They are also used in fields like medicine, where they can help determine the rate of change of a patient's condition.

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