Question

If W = xy + yz + z, find directional derivative of W at (1,-2,0) in the direction towards the point (3,6,9).

(a) -0.6

(b) -0.7

(c) -0.8

(d) -0.9

The question was posed to me by my school principal while I was bunking the class.

My question comes from Gradient of a Function and Conservative Field topic in section Vector Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (c) -0.8

For explanation I would say: The gradient of W is = y ax + (x+z) ay + (y+1) az

At (1,-2,0) the gradient of the function W is -2 ax +  ay –  az

\(\frac{dW}{dl} = \)(Gradient of W ) . al

\(= \frac{(-2,1,-1).(3,6,9)}{11.22} \)

\(= -0.8.\)