-1

In an certain question my teacher asked to find the maximum force. She said that the maximum force in electrostatics means $\frac{dF}{dx}=0$. Why is it like that?

Qmechanic
  • 201,751
gksingh
  • 415
  • The maximum(more precisely extremum) of any analytic function $f(x)$ means $\frac{df}{dx}=0$ – Ali Jul 03 '13 at 05:15
  • 3
    You need also $\frac{d^2F}{dx^2}<0$ at the extremum in order for that extremum to be a maximum. – user5402 Jul 03 '13 at 08:08
  • While plotting a graph of F v/s x, and the graph reaches a maximum value, the tangent at THAT maximum WILL be parallel to the x axis! Try it out yourself - pen + paper. This implies slope = 0, and slope is nothing but $\frac{df}{dx}$. – mikhailcazi Jul 03 '13 at 13:10
  • 5
    I'm voting to close this question as off-topic because that's a mathematics question, not physics. – stafusa Apr 26 '18 at 07:29

3 Answers3

6

Pretty basic result from elementary calculus, nothing to do with electrostatics.

enter image description here

Abhimanyu Pallavi Sudhir
  • 6,140
  • Edit accepted. (hurray unilateral decision making ;) Feel free to retag as you see fit, and then feel free to flag this comment for deletion. (or it seems to have been retagged anyway...) –  Jul 03 '13 at 05:40
3

This isn't a general principle of physics - it's just an instance of single-variable calculus. Presumably you have some 1-dimensional setup, where at each point $x$ you can calculate the force $F$. Then, assuming $F$ is a differentiable function of $x$, any local maximum of $F$ must be at a point such that $F'(x) = 0$. Of course, $F'(x) = 0$ is not sufficient, for it also describes local minima, etc. Moreover, even if there is only one local maximum, this is only guaranteed to be a global maximum if you have some other piece of information lying around such as "$F \to 0$ for $x$ sufficiently far away."

0

As shown in the graph There is no any point except pt M in the graph which may have maximum value than M And at the pt M if we draw a tangent then we will find the slope of tangent zero i e dy/dx =0 That's why if we called to find maximum value then We have to solve dy/dx=0 enter image description here

Md Aslam
  • 1