Suppose that the temperature at the point (x,y,z) is given by the formula
$$W(x,y,z)=100−x^2−y^2−z^2$$

The units of distance in space are in meters

a)find the rate of change of temperature at the point (3, -4, 5) if we start moving at the speed of one meter per second on the line of symmetric equations
$$\frac{x−3}{3}=\frac{y+4}{4}=z−5$$

b) In what direction does W increase most rapidly at the point (3,-4,5)?

c)what is the maximal value of the directional derivative at (3,-4,5)

Question

Suppose that the temperature at the point (x,y,z) is given by the formula 
$$W(x,y,z)=100−x^2−y^2−z^2$$

The units of distance in space are in meters 

a)find the rate of change of temperature at the point (3, -4, 5) if we start moving at the speed of one meter per second on the line of symmetric equations 
$$\frac{x−3}{3}=\frac{y+4}{4}=z−5$$

b) In what direction does W increase most rapidly at the point (3,-4,5)?

c)what is the maximal value of the directional derivative at (3,-4,5)

richyw · Answer

so the answer says:

the direction is $\vec{v}=(3,4,1)$

How did they figure this out? I know I need to find the gradient but I can't figure out the direction!