Convert a derivative back to original function

Click For Summary
SUMMARY

The discussion centers on converting the derivative function f'(x) = 5x^2 + 7x - 3 back to its original function f(x). The user attempted integration by incorrectly modifying terms, resulting in f(x) = (5/3)x^3 + 7x^2 - 3x. The correct approach involves recognizing that integration is the process being applied, and any constant can be added to the function without affecting the derivative. The conversation emphasizes the importance of understanding calculus concepts, particularly integration and differentiation.

PREREQUISITES
  • Understanding of calculus concepts, specifically derivatives and integrals.
  • Familiarity with polynomial functions and their properties.
  • Knowledge of integration techniques and rules.
  • Ability to differentiate functions to verify results.
NEXT STEPS
  • Study the Fundamental Theorem of Calculus to understand the relationship between differentiation and integration.
  • Learn integration techniques for polynomial functions, including power rule integration.
  • Practice verifying integration results by differentiating the obtained functions.
  • Explore online resources such as Khan Academy or Paul's Online Math Notes for additional calculus practice.
USEFUL FOR

Students studying calculus, particularly those tackling integration and differentiation problems, as well as educators looking for examples of common mistakes in these concepts.

Ishtar
Messages
10
Reaction score
0
Homework Statement

f'(x) = 5x^2 + 7x -3

The attempt at a solution

i divided 5 by 3 to get 5/3
added 1 to exponent of 5x^2
made 7x to 7x^2 and -3 to -3x

to get

f(x) = 5/3 x^ 3 + 7x^2 - 3xi get this answer, but is there and other way to get the original function and other possible answers (or a helpfull website related to this)
 
Last edited:
Physics news on Phys.org
The middle term is 7/2 x^2.

You can confirm your answer by differentiation back to f'(x).

Note that you could also add any number to your expression and you would still get the same derivative, because, e.g. d/dx 42 =0.

You're actually doing 'integration', though you may not know it yet. Wikipediate or Google it.
 
You said you "made 7x to 7x^2 and -3 to -3x" but you didn't do that in your answer.

Believe it or not, derivatives and "anti- derivatives" are calculus, not "pre"- calculus. I'm going to move this to the calculus homework forum.
 
oh yea, sry, and thanks for your answers
 

Similar threads

Limits...what am I doing wrong ? (Without hopital)
  • · Replies 2 ·
Replies
2
Views
1K
Question on Two Differentiation Techniques
  • · Replies 25 ·
Replies
25
Views
2K
Find the derivative of the given function
  • · Replies 4 ·
Replies
4
Views
2K
How Do You Simplify and Analyze Taylor Polynomials for Higher Degree Functions?
  • · Replies 5 ·
Replies
5
Views
2K
Odd/even function and critical points
  • · Replies 4 ·
Replies
4
Views
3K
Finding the max/min values of this function?
  • · Replies 11 ·
Replies
11
Views
2K
Determining domain for C^1 function
  • · Replies 4 ·
Replies
4
Views
1K
Linear Approximation of F(x) at x=1.001
  • · Replies 3 ·
Replies
3
Views
2K
Finding the Fourier Series of a step function
  • · Replies 5 ·
Replies
5
Views
3K
Cauchy-Riemann Condition Verification for f(z) = z^3-5iz+√7
  • · Replies 11 ·
Replies
11
Views
3K