Let $f ( x , y ) = 3 y ^ { 2 } + 2 x y$

question 5

Essay

Let $f ( x , y ) = 3 y ^ { 2 } + 2 x y$ Use the appropriate partial derivative to find the slope of the cross-section at the given point.
(a)The cross-section f(x, 2)at the point (3, 2).
(b)The cross-section f(1, y)at the point (1, -2).

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Definitions:

Trapezius Group

The trapezius muscle group is a large muscle extending from the neck to the mid-back and across the shoulders, involved in moving, rotating, and stabilizing the scapula (shoulder blade) and extending the neck.

Vastus Intermedius

A deep muscle in the anterior compartment of the thigh, part of the quadriceps femoris group, lying between the vastus lateralis and vastus medialis.

Quadriceps Femoris

A significant muscular grouping, consisting of four dominant muscles located at the front of the thigh, crucial for extending the knee.

Ventrolateral Surface

Refers to the surface of an anatomical structure that is both toward the belly and the side.