cal3

posted by .

Consider the function f(x,y)=xy+xz+yz+4 at point p=(2,-1,1)
a)find the unit vector in direction of p.
b) find the directional derivative at p in the direction of <0,-1/(sqrt2),-1/(sqrt2)>

  • cal3 -

    |p| = √(4+1+1) = √6
    u= p/|p| = (2/√6,-1/√6,1/√6)

    Now, with u = <0,-1/√2,-1/√2)>
    ∇<sub<uf = ∇f•u
    = (y+z)(0) + (x+z)(-1/√2) + (x+y)(-1/√2)
    = (0)(0) - 1/√2 (2+1) - 1/√2 (2-1)
    = -4/√2 = -2√2

  • cal3 -

    Oh crap typo error, should read find the unit vector in direction of maximum increase of f in the direction of P.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    I have to find an exact solutions on the interval [0,pi) for both of these problems-- 1) 2sin2x = sqrtx and 2) 1-2sqrt2 sinxcosx = 0 I know this much: 1) sin2x = (sqrt x)/2 = 2sinxcosx = (sqrt x)/2 What do I need to do next?
  2. Calculus Help!!!!

    Fnd the derivative if y=x^(1+sqrt2) Is this right (1+sqrt2)/(x) x^(sqrt2)
  3. Math

    1)Find the standard deviation of the data set to the nearest tenth. (21,13,18,16,13,35,12,8,15) A)16.8 B)7.8 C)7.3 D)5.7 I chose C mean = 21+13+18+16+13+35+12+8+15/9 16.8 variance = (21-16.8)^2 = 17.64...did that with the rest and …
  4. Algebra II (check)

    Assume that no denominator equals 0. sqrt12 - sqrt18 + 3sqrt50 + sqrt75 = (sqrt2^2*3) - (sqrt2*3^2) + (3sqrt2*5^2) + (sqrt3*5^2) = (sqrt2^2*sqrt3) - (sqrt3^2*sqrt2) + (3sqrt5^2*sqrt2) + (sqrt5^2*sqrt3) = (2*sqrt3) - (3*sqrt2) + (3sqrt5*sqrt2) …
  5. Calc

    The directional derivative of z = f(x,y) at (2,1) in the direction toward the point (1,3) is -2/sqrt(5), and the directional derivative in the direction toward the point (5,5) is 1. Compute dz/dx and dz/dy at (2,1). I have no idea …
  6. Calc

    "Let f(x,y)=2(x^2)y-(y^3)+x-4. a) Find the local linearization of f at (3,1) b) Compute the directional derivative of f at (3,1) in the direction towards the point (-2,3). At (3,1), is the function f increasing or decreasing in the …
  7. cal3 please help not too hard of a problem

    Consider the function f(x,y)=xy+xz+yz+4 at the point P=(2,-1,1) Find the unit vector in direction of maximum increase of f in the direction of p. I know the magnitude of p=sqrt6 how do i find this?
  8. calculus

    Find a unit vector U such that the rate of change of f in the direction of U at the given point is maximum. point being (3,5,pi) I know hos to do this when given a direction but since im asked to ind the unit vector first it kinda …
  9. Precalculus

    Given: f(x) = X^2-x evaluate: f(sqrt2 + 3) I have worked out this and am stuck: (sqrt2+3)^2 - (sqrt2+3) (sqrt2+3)*(sqrt2+3)- (sqrt2 +3) (sqrt2)^2+ 3sqrt2 +3sqrt2+ 9- (sqrt2+3) 2+6sqrt2 +9-sqrt2-3 and am stuck or wrong here. Ans= SQRT2+6sqrt2 …
  10. AP Calculus

    For the function y=4-2x^2+1/6x^4 find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points of inflection Concave …

More Similar Questions