Question

A function \( f \) and its first and 2nd partial desivatives are evaluated at \( (2,-1) \). the values are \( f=3, \frac{\partial f}{\partial x}=4, \frac{\partial f}{\partial y}=-3 \), \[ \frac{\partial^{2} f}{\partial x^{2}}=1, \frac{\partial^{2} f}{\partial x \partial y}=2, \frac{\partial^{2} f}{\partial y^{2}}=-1 . \] (a) Stater the and order taylor polymonial. generated by \( f \) about \( (2,-1) \) (b) Estimate \( f(1.8,-0.9) \) (c) verify that the taylor polynomial and have identical values at \( (2,-1) \) (d) verify that the 1st partial derivateine of the Taylor polynomial and \( f \) are identical at \( (2,-1) \) e) Verify that the 2nd Partial devivativie of the taylor polymomial and \( f \) are identical at \( (2,-1) \)

          A function \( f \) and its first and 2nd partial desivatives are evaluated at \( (2,-1) \). the values are \( f=3, \frac{\partial f}{\partial x}=4, \frac{\partial f}{\partial y}=-3 \),
\[
\frac{\partial^{2} f}{\partial x^{2}}=1, \frac{\partial^{2} f}{\partial x \partial y}=2, \frac{\partial^{2} f}{\partial y^{2}}=-1 .
\]
(a) Stater the and order taylor polymonial. generated by \( f \) about \( (2,-1) \)
(b) Estimate \( f(1.8,-0.9) \)
(c) verify that the taylor polynomial and have identical values at \( (2,-1) \)
(d) verify that the 1st partial derivateine of the Taylor polynomial and \( f \) are identical at \( (2,-1) \)
e) Verify that the 2nd Partial devivativie of the taylor polymomial and \( f \) are identical at \( (2,-1) \)

A function f and its first and 2nd partial desivatives are evaluated at (2,-1). the values are f=3, (∂ f)/(∂ x)=4, (∂ f)/(∂ y)=-3,

(∂^2 f)/(∂ x^2)=1, (∂^2 f)/(∂ x ∂ y)=2, (∂^2 f)/(∂ y^2)=-1 .

(a) Stater the and order taylor polymonial. generated by f about (2,-1)
(b) Estimate f(1.8,-0.9)
(c) verify that the taylor polynomial and have identical values at (2,-1)
(d) verify that the 1st partial derivateine of the Taylor polynomial and f are identical at (2,-1)
e) Verify that the 2nd Partial devivativie of the taylor polymomial and f are identical at (2,-1)

Added by Pilar R.

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