Understanding the Turning Point and Asymptote of a Calculus Sketch

In summary, the conversation is discussing a mathematical problem involving finding the first and second derivatives of the equation y=x+4/(x-1). The minimum turning point is located at (1/2, 15/4) and there are no points of inflexion. There is also an asymptote at x=1. The conversation also touches on finding the value of y at x=0 and the value of x at y=0, as well as the direction of the asymptote at x=1.
  • #1
aricho
71
0
hey guys, having trouble with this one:

y=x + 4/(x-1)

i have found 1st and 2nd derivatives.

Minimum turing point at (1/2, 15/4) and there are no points of inflexion. there is an asympote at x=1...right.

This line is more than just that though isn't it? how can u tell that you got all the lines? we did it in class with limits but i kinda didnt get it.


All help is apprecaited...thanks!
 
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  • #2
How about the simple questions like:

What's the value of y at x=0?

and

What's the value of x at y=0?

(You are correct about the asymptote at x=1 - which direction does it go?)

I also get different x-values for the turning point(s).
 
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Related to Understanding the Turning Point and Asymptote of a Calculus Sketch

1. What is a calculus sketch question?

A calculus sketch question is a type of problem in which a function or curve is given and the goal is to graph or sketch the curve by using calculus concepts such as derivatives and integrals.

2. How do I approach a calculus sketch question?

The first step is to identify the given function and its domain. Then, use calculus concepts such as derivatives and integrals to find key points on the curve, such as critical points, inflection points, and intercepts. Finally, use these points to sketch the curve.

3. What is the purpose of solving a calculus sketch question?

Solving a calculus sketch question helps develop a deeper understanding of calculus concepts and their applications. It also improves problem-solving skills and prepares students for more complex calculus problems.

4. What are some common mistakes to avoid when solving a calculus sketch question?

Some common mistakes to avoid include not considering the domain of the function, not finding all key points on the curve, and misinterpreting the behavior of the curve at certain points. It is also important to check for accuracy and ensure that the final sketch accurately represents the given function.

5. Can I use a calculator to solve a calculus sketch question?

While a calculator can be helpful in finding derivatives and integrals, it is important to have a solid understanding of calculus concepts and be able to solve problems by hand. Using a calculator should only be used as a tool to check answers or to save time on more complex calculations.

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