Find $x$ for a given derivative value.

Question

Given a function $ y=f(x)$. I know that the function is continuous, now for a given $y^{'}_0$, I have to find $x$ such that $\dfrac{\mathrm df(x)}{\mathrm dx} = \dfrac{dy}{dx}=y_0^{'}$ at that $x$.

To solve this problem numerically i tried

$g(x) = \frac {f(x+h) - f(x-h)}{2h} - y_0^{'} = 0$

so $f(x+h) - f(x-h) = 2h \cdot y_0^{'} $

but this is not and an efficient method since it depends a lot on choice of $h$ and I have to solve it multiple times..

Is there a better way?

Hi and welcome to our community! Please try to typeset your posts using MathJax. — Rebellos, May 10 '20 at 07:17
A continuous function is not necessarily differentiable. Moreover, without more information about $f$, trying to find $x$ such that $\frac{df}{dx}(x)=y_0$ is almost an impossible task... — Isaac Ren, May 10 '20 at 07:19
f is differentiable. and also i have to solve it numerically — Pramod Azad, May 10 '20 at 07:26
Used prime for denoting given derivative value as convention and edited. Switched to a simpler example. Hope alright. — Narasimham, May 11 '20 at 10:02

Narasimham · Answer 1 · 2020-05-11T10:07:14.183

1

If $y(x)=f(x)= x^2/4 +5,\, y_0^{'}=1.1 $ are given then by direct differentiation:

$$ y'(x_0)=x_0/2 = y_0^{'}=1.1 \rightarrow x_0= 2.2 $$

which can be solved numerically.

edited May 11 '20 at 10:07

answered May 10 '20 at 07:46

Narasimham

40,495

No, But we are certain that the df/dx takes the value y0 at some x – Pramod Azad May 10 '20 at 08:01
Can you use Runge-Kutta numerical methods to solve for $y'(x)= yo?$ – Narasimham May 10 '20 at 08:17
In my case the function cannot be directly differentiated. the differentiation is calculated numerically. this whole problem I have to solve numerically. – Pramod Azad May 11 '20 at 11:37
In reply to IsaacRen you stated that $f$ is differentiable. – Narasimham May 11 '20 at 12:56

Find $x$ for a given derivative value.

1 Answers1