How to find derivative to a function

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SUMMARY

The discussion centers on finding the derivative of the function F(x) = x√(1-x) and determining its absolute minimum and maximum. Users emphasize the necessity of applying the product rule for differentiation, specifically the formula (fg)'(x) = f'(x)g(x) + f(x)g'(x). Participants also highlight the importance of providing initial work to facilitate assistance and clarify any potential confusion regarding variable notation.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly differentiation.
  • Familiarity with the product rule for derivatives.
  • Knowledge of how to find critical points for optimization.
  • Ability to interpret mathematical notation accurately.
NEXT STEPS
  • Study the product rule in detail, including examples and applications.
  • Learn how to find critical points and determine absolute extrema of functions.
  • Explore the implications of variable notation in mathematical expressions.
  • Practice solving similar derivative problems to reinforce understanding.
USEFUL FOR

Students studying calculus, mathematics enthusiasts, and anyone seeking to improve their skills in differentiation and optimization techniques.

cldance5678
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Hi,
I am new to the forum and having a problem solving this equation any help would be apprehended.

The problem is F(x)=X√1-x
Need to find derivative then absolute min and max.

P.S please let me know if i am posting the right way.

Thanks
John
 
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Hey John, Welcome to physicsforums!
In this Forum, the idea is to give a good attempt at the problem, and write down your working, and if you don't manage to get to the right answer, then people offer advice. So we definitely need more information on what you are getting stuck with in this problem. Also, is the function mean to be: [itex]x \sqrt{1-x}[/itex] I wasn't sure if that big X was meant to be a different variable, or the same as the little x ?
 
cldance5678 said:
Hi,
I am new to the forum and having a problem solving this equation any help would be apprehended.

The problem is F(x)=X√1-x
Need to find derivative then absolute min and max.

P.S please let me know if i am posting the right way.

Thanks
John
Assuming that you meant ##x\sqrt{1-x}##, you will need to use the product rule: ##(fg)'(x)=f'(x)g(x)+f(x)g'(x)##.

This is really all we can tell you at this point. We will only offer hints, not complete solutions. You are also expected to post your work up to the point where you get stuck. When you start a new thread, you should use the template that's provided for you. (If you preview, another copy of the template is inserted. This is a known bug that we don't know how to fix. So you will just have to delete the extra template).
 

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