Trying to find the Lagrange's mean value theorom constant

Question

Soham Patil 2021-10-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1562036-trying-to-find-the-lagrange-s-mean-value-theorom-constant

回答： Nipun 2024-4-16

在 MATLAB Online 中打开

The script i wrote is

But i get these error

R =

root(z^4 + 2*z^2 - 5*z + 1, z, 1)

root(z^4 + 2*z^2 - 5*z + 1, z, 2)

root(z^4 + 2*z^2 - 5*z + 1, z, 3)

root(z^4 + 2*z^2 - 5*z + 1, z, 4)

Error using symengine

Unable to prove 'imag(root(z^4 + 2*z^2 - 5*z + 1, z, 1)) == 0 & 0 < real(root(z^4 + 2*z^2 - 5*z + 1, z, 1)) & real(root(z^4 + 2*z^2

- 5*z + 1, z, 1)) < 2' literally. Use 'isAlways' to test the statement mathematically.

Error in sym/subsindex (line 949)

X = find(mupadmex('symobj::logical',A.s,9)) - 1;

Error in sym/subsref (line 997)

R_tilde = builtin('subsref',L_tilde,Idx);

Error in exp_lmvt (line 14)

S=R(imag(R)==0&real(R)>a&real(R)<b)

clear
clf
clc
syms x
f(x)=input('Enter the function')
a=input('Enter the left endpoint')
b=input('Enter the right endpoint')
f_1(x)=diff(f,x)
fa=f(a)
fb=f(b)
m=(fb-fa)/(b-a)
C=m*(x-a)+fa
R=solve(f_1(x)==m,x)
S=R(imag(R)==0&real(R)>a&real(R)<b)
T=m*(x-S)+f(S)
fplot(f)
hold on
disp(char(S))
plot(a,f(a),'.','MarkerSize',25)
plot(b,f(b),'.','MarkerSize',25)
plot(S,f(S),'.','MarkerSize',25)
fplot(C)
fplot(T)
hold off

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Answer 1

Nipun 2024-4-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1562036-trying-to-find-the-lagrange-s-mean-value-theorom-constant#answer_1442126

Hi Soham,

I understand that you intend to find the constant "c" in Lagrange's mean value theorem given an equation using MATLAB.

Based on the given code, your input function should only be dependent on "x" and not any other variable, since only "x" is defined as a symbolic variable.

On running the code, with "x^2" as the function and "2", "5" as the left and right endpoints respectively, I get the follwing output as expected:

f(x) =

a = 2

b = 5

f_1(x) =

fa =

4

fb =

25

m =

7

C =