Find the Derivative of the Function at P0 in the Direction

question 225

Multiple Choice

Find the derivative of the function at P0 in the direction of u.
- $$f ( x , y , z ) = 4 x + 8 y - 7 z , \quad P _ { 0 } ( - 7,10 , - 10 ) , \quad \mathbf { u } = 3 \mathbf { i } - 6 \mathbf { j } - 2 \mathbf { k }$$

• A) \(\frac { 2 } { 7 }\)
• B) \(\frac { 10 } { 7 }\)
• C) \(- \frac { 46 } { 7 }\)
• D) \(- \frac { 22 } { 7 }\)

---

Definitions:

Low-impedance Ground

A grounding method or system that has a very low electrical resistance path to the earth to ensure safety and reduce the risk of electrical shock or fire.

Electrostatic Field

An electrostatic field is a region surrounding a charged particle or object within which a force would be exerted on other charged particles or objects.

I/O Signal Wiring

I/O signal wiring involves the physical connections used to link input and output devices to the control system, enabling data and control signal transmission.