2. (a) Find the maximum and minimum rates of change of f (x, y, z) = e*yz+1 at (0, -1,1). (b) Find the directions in which f(x,y,z) = exyz+1 is increasing and decreasing most rapidly at (0, –1,1) (c) Fill in the blanks. = exyz+1 has a maximum rate of change of. • f(x, y,z) direction of in the • f(x, y, z) direction of. exyz+1 has a minimum rate of change of in the (d) Find the unit vector in the direction of maximum increase of f (x, y, z) = exyz+1 at (0, –1,1). %3D

Q: the temperature (in F) at point (x,y)(measured in miles) is given by  T(x,y)=80-x4 +2x2 y-y2 How…

A:

Q: Given the function z = f(x,y) = (x^2-1)(y-2): find the equation for the trace when x=2, the trace…

A: The objective of this question is to find the equations for the traces of the function z = f(x,y) =…

Q: Find the directions in which f increases and decreases most rapidly at point P. Then find the…

A: As per guidelines, we will solve first question only.

Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

A:

Q: 2(b) Just the answer please. What is the instantaneous rate of change of the function defined by…

A: The given problem is to find the instantaneous rate of change of the function at given point. Given…

Q: Find f(-1,1,0) f(x,y,z)=(2xy-y^2+z)/(x^2+3xy+z)

A:

Q: Find maximum rate of change of f at the given point. f(x,y)=sin(xy), (1,0)

A:

Q: Suppose f(x) = "6r V1+f dt.

A: Topic = Integration

Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 300e-x²-3y² - 9z² where T is measured…

A:

Q: Q/ show that f(Z) = |Z|2= x² + y² has a derivative only at the origin

A:

Q: Find the x and y coordinates on the graph of f (x) = x³ - 3x where the tangent is horizontal. (A)…

A:

Q: Which among the following functions has the derivative of h' (z) %3D (z - 2) On(z) %3D Oh(z) %3D (2…

A:

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A:

Q: f(z)=ze^tz/z^2+1 for this function find the Rez(f(z),i) and Rez(f(z),-i) .

A:

Q: Q6// Find the value of first and second derivative for the equation x² + xy - y² = y/x,at (1,1)

A:

Q: If (X, d_{1}) and (Y, d_{2}) are metric spaces, we define d: (X × Y ) × (X × Y ) \rightarrow R by…

A: Let X be a nonempty set with a mapping d:X×X→R is said to be a metric space if mapping d…

Q: Evaluate the value of ‘a’ if the first derivative of m(x,y,z)=4-ax^2-2y^2, with respect to the…

A: Consider: mx,y,z=4-ax2-2y2 and mx1,2,3=-2. Solve for a. Calculate mxx,y,z by applying…