What is the derivative of f(x)=-x^3+4x^2 at (-1,5) using the limit definition?

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Homework Help Overview

The discussion revolves around finding the derivative of the function f(x) = -x^3 + 4x^2 at the point (-1, 5) using the limit definition of the derivative. Participants are exploring the application of this definition and clarifying the evaluation of the function at the specified point.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the limit definition of the derivative and the correct evaluation of f(-1). There are attempts to simplify the limit expression and questions about the correct form of the derivative. Some participants express confusion about the algebra involved in the limit process.

Discussion Status

The conversation is ongoing, with participants providing guidance on the correct evaluation of f(-1) and the limit definition. There is a recognition of the need to clarify algebraic steps and the importance of correctly applying the limit definition. Multiple interpretations of the problem are being explored.

Contextual Notes

Participants are working under the constraints of a homework assignment that requires the use of the limit definition for derivatives, despite some suggesting alternative methods that may be more efficient.

  • #61
sutupidmath said:
Well, with shortcut here i meant to use the other alternative of the deff. of the derivative,

\lim_{x\rightarrow -1}\frac{f(x)-f(-1)}{x+1} it takes you much faster to the answer.

I'd prefer not to resort to synthetic division.
 
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  • #62
yourdadonapogostick said:
I'd prefer not to resort to synthetic division.

thats what i did at first...
and i got the -x^3+4x^2-5 to go into (x+1)(-x^2 +5x -5)/(x+1) and so the (x+1) canceled...
but when i told everyone that i got -x^2 +5x -5 for my answer they said that there was no x+1 in the numerator and i had to go through the other equation...
and i just realized if i would have plugged in the -1 for all the x's i would have gotten -11 baack in like post number 15 XD
 
  • #63
sutupidmath said:
Well, you will learn this stuff, don't worry about that. I didn't know you were still in high school...lol...

is this for like mostly college people or something?
 
  • #64
Precal_Chris said:
is this for like mostly college people or something?


Well, one usually learns this stuff in calc 1. So, i wrongly guessed...lol..
 
  • #65
Precal_Chris said:
is this for like mostly college people or something?

I learned calculus in high school and I never went to college. I did join the military as a Naval Nuclear Mechanic, though.
 
  • #66
oh yeah she said this last six weeks we are going to be doing a lot of calc stuff
 

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