Calculus Chapter 12.3 Question 6

Evaluate fx(x,y) and fy(x,y)at the indicated point.

  1. \[f(x,y) = x^3 -3x +y^2 -6y \] at (-1,3)

\[\frac{\delta f}{\delta x} = 3x^2 -3 \] \[ f_x(-1,3) = 3(-1)^2 - 3 = 0\]

\[\frac{\delta f}{\delta y} = 2y^ -6 \]

\[ f_y(-1,3) = 2(3) - 6 = 0\]

Question 11

find fx, fy, fxx, fyy, fxy and fyx.

\[ f(x,y) = \frac {x} {y} \]

\[f_x = \frac {1} {y} \] \[ f_y = \frac {-x}{y^2} \]

\[ f_{xx} = 0 \] \[ f_{yy} = \frac {-2x}{y^3} \]

\[ f_{xy} = \frac {-1}{y^2} \]

\[ f_{yx} = \frac {-1}{y^2} \]

Most Valuable Elements in the Course

-Refresher of math 
-Course concepts is aligned towards machine learning and helpful for data analysis.