Suppose Z = X1/3Y 2/3. Graph the corresponding partial derivative of Z with respect to X,...

Suppose Z = X1/3Y 2/3. Graph the corresponding partial derivative of Z with respect to X, holding Y constant.

Justify the direction and curvature of your graph using the signs of the relevant derivatives. Passing requires 1) correctly differentiating the function; 2) identifying the correct derivative(s) to determine direction; 3) identifying the correct derivative(s) to determine curvature; 4) correctly interpreting the signs of these derivatives to graph the function; and 5) graphing the function and labelling the axis.

Expert Solution

Rahul Sunny answered 2 years ago

Compute the directional derivative of T(x,y,z)=200e^(-x^2-3y^2-9z^2) at the point (2,-1,2) in the direction toward the point...

Compute the directional derivative of T(x,y,z)=200e^(-x^2-3y^2-9z^2) at the point (2,-1,2) in the direction toward the point (3,-3,3). What is the maximum rate of change of T at the point (2,-1,2)? I have solve this by mathematica...

Solve for x,y,z using the inverse if possible. x+2y+5z=2 2x+3y+8z=3 -x+y+2z=3

1. For z=x^2-xy^2 find: a. the gradient for z; b. the directional derivative in direction of...

1. For z=x^2-xy^2 find: a. the gradient for z; b. the directional derivative in direction of <3,-1>; c.the approximation for Δz when taking a Δs =0.05 step from (1,2) in direction of <3,-1>; d. the approximation to the maximum Δz possible when taking a Δs =0.05 step from (1,2).

(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3),...

(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3), x2 = lnx3. find ∂f/∂x3, and df/dx3.

Find the z-score corresponding to a score of X= 40 and the X value corresponding to...

Find the z-score corresponding to a score of X= 40 and the X value corresponding to z = 0.25 for each of the following distributions. a. μ = 50 and σ = 20 b. μ = 50 and σ = 4 c. μ = 30 and σ = 8 d. μ = 30 and σ = 4

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x +...

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x + 1)(x + 5). Determine the intervals of x for which the function of f is increasing and decreasing Explain why a positive value for f" (x) means the graph f(x) is increasing For f(x) = 2x2- − 3x2 − 12x + 21, find where f'(x) = 0, and the intervals on which the function increases and decreases Determine the values of a, b, and...

1. Find the partial derivatives of f(x,y) = xe^(4xy) fx=? fy=? 2. Find the partial derivative...

1. Find the partial derivatives of f(x,y) = xe^(4xy) fx=? fy=? 2. Find the partial derivative of f(x,y) = sqrt(x^3 + 4y^5) fx=? fy=?

1. U ( x 1 , x 2 ) = 2 x1 + 3 x 2...

1. U ( x 1 , x 2 ) = 2 x1 + 3 x 2 If the price of good 1 is $4/unit, the price of good 2 is $5/unit , and income is $20... What is this person's optimal consumption level for good 1? 2. U( x 1 , x 2 ) = 5 x1 + 3 x2 If the price of good 1 is $2/unit, the price of good 2 is $1/unit , and income is $10......

Find volume of D enclosed by surfaces z = x² + 3y² and z = 8...

Find volume of D enclosed by surfaces z = x² + 3y² and z = 8 - x² - y²

The reflection of the plane 2x-3y+4z-3=0 in the plane x-y+z-3=0 is the place

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