Gradient Problem: Find Rate of Change, Direction, & Maximum Increase

[munkhuu1]

Homework Statement

T(x,y,z)=8x^2-7xy+7xyz
a. find the rate of change of t at point p(-1,1,-1) in the direction u=<8,10,-8>
b. which direction does the temperature increase fastest
c. find the maximum rate of increase at P.

Homework Equations

gradient of T=(16x-7y+7yz, -7x+7xz, 7xy)

The Attempt at a Solution

a. i multiplied gradient by unit vector <8,10,-8>/square root of 228 and i got -2.914
please tell if this is right.
b. i just found gradient T(-1,1,-1)=<-30,14,-7>
c. i found the magnitude of b which was 33.84

 

[BruceW]

yep, all good. Nice work.