9(-1,2,-4)-5, 9(-1,2,-4)-2 y(-1,2,-4-3 and 9.(-1,2,-4) 6 Answer the following qu

Question

9(-1,2,-4)-5, 9(-1,2,-4)-2 y(-1,2,-4-3 and 9.(-1,2,-4) 6 Answer the following questions, and carefully justify all your answers. solve only (e) and (f) (c) Which of the following objects exist(s)? Justify your answers, and find an equation for the ones that exist. The tangent plane to the graph of g(x, y, 2) at (-1,2,-4 The tangent plane to the level set g-5 at (-1,2,-4). (d) Find all possible values of c, if any, such that the vectori--3i+3+ck is tangent to the level set g 5 (e) At the point (-1,2,-4), what is the rate of change of g along a vector that intersects the plane from (g(z, y, 2)2. What relationship do you see between part (c) at a 40° angle and is closer to ?g than it is to-Ty? (f) Find the partial derivatives of the function h(, y, 2) the partial derivatives of h and those of g? Why does this make sense?

Explanation / Answer

e)The determined plane from part (c) is 2x-3y+6z+32=0; The angle between the intersecting plane is 400. So the x and y slopes of the intersecting plane will be (-2/6)(tan 400)=-0.28 and (3/6)(tan 400)=0.42.

The intersecting plane will be ; z=-0.28x+0.42y+k (k is any constant);

So the rate of change of g at (-1,2,-4) along the vector intersecting the plane from part (c) at an angle of 400 will be

(-0.28)(-1)+(0.42)(2)+(-1)(-4)=5.12 units.

f) The relationship between the partial derivatives of h and g will be hx=2gx , hy=2gy , hz=2gz.

Explanation:

The function given; h(x,y,z) =(g(x,y,z))2 .

partial derivatives of h(x,y,z) interms of x, y and z are denoted by hx , hy , hz respectively.

partial derivatives of g(x,y,z) interms of x, y and z are denoted by gx , gy, gz respectively.

partial derivatives of (g(x,y,z))2 = 2 ( partial derivatives of g(x,y,z)).

Related Questions

Navigate

• Browse (All)
• Browse 9
• Subjects

---

---

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