Business
Engineering
Math
Science
Social ScienceFind the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directionsf(x.y) x2 +xy+y2Po-3,-1)The direction in which the given function f(x,y) x xy+yincreases most rapidly at Po(-3, -1) is u(Type exact answers, using radicals as needed.)
Find the direction f(x,y) increases and decreases most rapidly at point P and find the derivatives of the functions in these directions (f(x,y) and P included in the image)
Image Transcriptionclose
Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions f(x.y) x2 +xy+y2 Po-3,-1) The direction in which the given function f(x,y) x xy+yincreases most rapidly at Po(-3, -1) is u (Type exact answers, using radicals as needed.)
Expert Answer
Consider the given function.
Image Transcriptionclose
f(x, y) x2 +xyy
To find the gradient of the function is the vector of partial derivatives.
Image Transcriptionclose
2x+y+0 af - 2x +y Ox At P(3,-1) =2(-3)+ (-1) axk--4) of -6-1 of exk-- =-7 Similarly g0+x+2y af x+2y At P,(-3,-1) =-3+2(-1) y\ --3-2 --1) --5 -3-1)
Therefore, the direc...
Image Transcriptionclose
af f Vf(x,y) axc f(x,y)-7i-5j
Math
Calculus
Other
Related Calculus Q&A
Q: Differentiate y = V910x У 3
A: Write expression of y using exponent.
Q: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 44...
A: Click to see the answer
Q: Which of the following functions are solutions of the differential equation y′′−9y′+18y=0?A. y(x)=e3...
A: The given differential equation is,
Q: Suppose that f(5) = 1, f '(5) = 9, g(5) = −5, and g'(5) = 2. Find the following values. (a) (fg)'...
A: Click to see the answer
Q: Find the derivative
A: Given,
Q: What does the nth term test determine for the summation of (e^n)/(e^n+n) from 0 to infinity?
A: We are given the expression,
Q: Find dy/dx
A: Given expression,
Q: 2. Describe each of the following with a parametrization. Be sure to indicate the possible values fo...
A: To determine:Part a) The parametric equation of circle.Part b) Parametric equation of a point.
Q: Evaluate the following limits: 5/(e^x)+7 as x approaches infinity 5/(e^x)+7 as x approaches negative...
A: Given:
