Suppose that f(x, y, z) is a function which has continuous second partial deriva

Question

Suppose that f(x, y, z) is a function which has continuous second partial derivatives, and define Q = -4 partial differential f/partial differential x + partial differential f/partial differential y - 5 partial differential f/partial differential z. Suppose also that partial differential^2 f/partial differential x^2 (0, 0, 0) = -0.075100, partial differential^2 f/partial differential y^2 (0, 0, 0) = 0.908000, partial differential^2 f/partial differential z^2 (0, 0, 0) = -0.044100. partial differential^2 f/partial differential x partial differential z (0, 0, 0) = -0.014700. Calculate, at (0, 0, 0), the value of 4 partial differential Q/partial differential x + partial differential Q/partial differential y + 5 partial differential Q/partial differential z. 5.47079 2.81764 3.8001 2.89725 5.26969 2.99861 2.6271 5.06134

Explanation / Answer

Given: Q = - 4 f x + fy - 5 fz

evaluate the expression : 4 Qx + Qy + 5 Qz = 4 [ - 4 fxx + fyx - 5 fzx ] + [ - 4 f xy + fyy - 5 fzy]

+ 5 [ - 4 fxz + fyz - 5 fzz]

= - 16 f xx + 4fyx - 20 fzx  - 4 fxy + fyy - 5 fzy - 20 fxz + 5 fyz - 25 fzz

= - 16 fxx + fyy  - 25 fzz [ as fxy = fyx and so on]

= -16 x - .0751 + .908 - 25 x - .0441

= 3 . 2121

   =

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.