Need help on this curve-sketching problem.

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In summary, the conversation revolves around someone asking for help with a problem and providing a function to sketch. The other person then provides information derived from the function, including its domain, x and y-intercepts, asymptote, end behavior, first and second derivatives, and points of inflection. A correction is made regarding a missed x-intercept and the conversation ends with gratitude.
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jzq
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Would someone please help me on this problem? I'm sorry if it is hard to read. I'm new to this forum and haven't had the time to read over the latex system guide. I just need to make sure the information that I got is correct. Thank you.

Sketch the graph of the function, using the curve-sketching guide.

Function: f(t)=3(t)^(4) + 4(t)^(3)

From this function, I derived this information (Please check):
Domain: all real #s
x-int: (0,0)
y-int: (0,0)
Asymptote: none
End Behavior: points up at both ends.
First Derivative: f'(t)=12(t)^(3) + 12(t)^(2)
Decreasing: (-infinity,-1)
Increasing: (-1,+infinity)
Relative Minima: (-1,-1)
This is where I think I messed up!
Second Derivative: f''(t)=36(t)^(2) + 24(t)
Concave Up: (0,+infinity), (-infinity,-2/3)
Concave Down: (-2/3,0)
Points of Inflection: (0,0), (-2/3,-16/27)
 
Last edited:
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  • #2
Perfect. Got the same thing.

EDIT: You missed one x-intercept at x = -4/3. Besides that, looks good.
 
  • #3
Jameson said:
Perfect. Got the same thing.

EDIT: You missed one x-intercept at x = -4/3. Besides that, looks good.
Thanks alot!
 

1. What is curve-sketching?

Curve-sketching is a mathematical technique used to graph a function or equation by analyzing its key features, such as intercepts, asymptotes, and critical points.

2. What is the purpose of curve-sketching?

The purpose of curve-sketching is to gain a visual understanding of a mathematical function or equation and to accurately represent its behavior.

3. What are the steps involved in curve-sketching?

The steps involved in curve-sketching include analyzing the function for key features, such as intercepts, asymptotes, and critical points, plotting points to create a rough sketch, and then refining the sketch by adding more points and accurately representing the behavior of the function.

4. What are the common challenges in curve-sketching?

Some common challenges in curve-sketching include identifying the key features of the function, choosing appropriate scales for the axes, and accurately representing the behavior of the function, especially near critical points and asymptotes.

5. How can I improve my curve-sketching skills?

Practice is the key to improving curve-sketching skills. It's important to familiarize yourself with different types of functions and their key features, and to regularly practice sketching them. You can also seek help from a tutor or use online resources for additional guidance and practice problems.

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