Question

What is the Lagrange’s Theorem?

Answer

Lagrange's Theorem is: $\mathrm{If }y=z+x\mathrm{ɸ}\left(y\right),$
$f\left(y\right)=f\left(z\right)+x\mathrm{ɸ}\left(z\right) f΄\left(z\right)+\frac{x^2}{\mathrm{2\; !}}\frac{d}{dz}\left[{\left\{\mathrm{ɸ}\left(z\right)\right\}}^{2}f΄\left(z\right)\right]+\mathrm{...}+\frac{x^n}{\mathrm{n\; !}}\frac{d^{n-1}}{d{z}^{n-1}}\left[{\left\{\mathrm{ɸ}\left(z\right)\right\}}^{n}f΄\left(z\right)\right]+\mathrm{...}$