let f(x,y)=x^2y(2-x+y^2)-4x^2(1+x+y)^7+x^3y^2(1-3x-y)^8 find the coefficient of x^5y^3

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Colby Messinger answered 2 years ago

Let f(x, y) = xy3 − x 2 + 2y − 1. (a) Find the gradient...

Let f(x, y) = xy3 − x 2 + 2y − 1. (a) Find the gradient vector of f(x, y) at the point (2, 1). (b) Find the directional derivative of f(x, y) at the point (2, 1) in the direction of ~u = 1 √ 10 (3i + j). (c) Find the directional derivative of f(x, y) at point (2, 1) in the direction of ~v = 3i + 2j.

1. a. Find the relative maximum and minimum values of f(x, y) = (3x^2) − (2y^2)...

1. a. Find the relative maximum and minimum values of f(x, y) = (3x^2) − (2y^2) b. Find the relative maximum and minimum values of f(x, y) = (x^3) + (y^3) − 6xy . The expression that you may need D = fxx(x0, y0)fyy(x0, y0) − (fxy(x0, y0))2

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which...

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which f is increasing/decreasing and identify any local extrema. (b) Find the intervals on which f is concave up/down and find any inflection points. B. Consider the function f(x) = sin(x) + cos(x). Find the absolute minimum and absolute maximum on the interval [−π,π].

Let f(x,y) = 3x^2 + 6xy a) find the rate of change of f at the...

Let f(x,y) = 3x^2 + 6xy a) find the rate of change of f at the point P(3,2) in the direction of u = [3,4] b) In what direction does f have the maximum rate of change? what is the maximum rate of change?

Find a general solution of the inhomogeneous equation y′′ + 2y′ + 5y = f(x) for...

Find a general solution of the inhomogeneous equation y′′ + 2y′ + 5y = f(x) for the following cases: (i) f(x) = 1 (ii) f(x) = x2 (iii) f(x) = e−x sin2x (iv) f(x) = e−x (v) sin2x

1. You are given the function f(x) = 3x^4 + 4x^3 a) Find the x and...

1. You are given the function f(x) = 3x^4 + 4x^3 a) Find the x and y- intercepts. b) Find the critical number(s) of f. c) Find the interval(s) of increase and decrease of f. d) Find the relative maximum and minimum value(s) of f. e) Find the hypercritical number(s) of f. f) Find the interval(s) of upward and downward concavity of f. g) Find the point(s) of inflection of f. h) Sketch the graph of f. 2. You are...

Calculate the all of the second order derivatives of f(x,y)=x^4 y- 〖3x〗^4 y^3+5y-10 Let be f(x,y,x)=2x^5...

Calculate the all of the second order derivatives of f(x,y)=x^4 y- 〖3x〗^4 y^3+5y-10 Let be f(x,y,x)=2x^5 yz^3-3x^(-4) y^3 calculate the f_xyz=? If f(x,y,z)〖=5e〗^(-xyz^6 ) +lnx calculate the f_yxz=? Let f(x,y)=cos(x^3 y) ise df/dx=? df/dy=? z=2x+y , x=sin(3t ) and y=cos(3t) using the chain rule calculate the dz/dt where t=π/2. Find the critical points of the f(x,y)=〖6x〗^2+12y^2+12x-24y and provide the information about the critical points obtained (if it is max, min or saddle point).

f(x,y) = 2/7(2x + 5y) for 0 < x < 1, 0 < y < 1...

f(x,y) = 2/7(2x + 5y) for 0 < x < 1, 0 < y < 1 given X is the number of students who get an A on test 1 given Y is the number of students who get an A on test 2 find the probability that more then 90% students got an A test 2 given that 85 % got an A on test 1

Find a unit vector normal to the level curve f(x,y) = -4x^2 -2y^2 + 5x +...

Find a unit vector normal to the level curve f(x,y) = -4x^2 -2y^2 + 5x + y at the point (1,-2)

y"-3y'+2y=4t-8 , y(0)=2 , y'(0)=7 y(t)=?

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