Question

The grad • at the point (1.-2.-1) for ^ (x, y, z) = 3x²y-y³z² is

• A. -12i – 9j - 16k
• B. -2i 7j - 8k
• C. -2i - 9j - 16k
• D. -12i - 7j - 16k

Answer 1

Answer:

A. -12i – 9j - 16k

f(x,y,z) = 3x²y - y³z² Δf(x,y,z) = (df/dx, df/dy, df/dz) df/dx= 6xy df/dy = 3x² - 3y²z² df/dz =(Δ) - y³×2z Δf = (6xy, 3x² - 3y²z², -2y³z) Δf(1,-2,-1) = (-12, -9, -16) The grad • at the point (1.-2.-1) for ^ (x, y, z) = 3x²y-y³z² is = -12I, -9j, -16k