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WeBWork is an innovative online homework system widely used by educational institutions worldwide. Its main goal is to help students better understand subjects like math and science. Additionally, WeBWork creates assignments personalized to students’ needs so students can have a more personalized learning experience.
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We Have Qualified Experts Capable Of Solving WeBWork Answers. See Below For Sample Answers To Challenging Questions And Solutions.
Q.1) Express revenue as a function of two quantity demand-price pairs and quantity, assuming that demand price is a linear function, where the quantity demand-pairs are (0,20) and (101,19), and the quantity is 148.
Ans. Revenue (q) =20q-1/101 Q^2
Revenue (148) = 2743.13
Q.2) The function is P1= (9,3) and P2= (3,2)
a. Give the 2 functions of one variable through P1 obtained by holding each variable constant
Ans.
f(9,y) = 81+18y+7y^2
f(x,3) = x^2+6x+63
b. Find the partial derivatives of the original function.
Ans.
f x( x, y ) = 2x+2y
f x( x, y ) = 2x+14y
c. Evaluate the partial derivatives at P1
Ans.
f x( 9, 3 ) = 24
f y( 9, 3 ) = 60
d. Give the equation of the tangent plane through P1
Ans.
f (3, 2) = -6
Q.3) The function is . P1= (8,3) and P2 = (4,9)
a. Give the 2 function of one variable through P1 obtained by holding each variable constant.
Ans.
f(8, y) = 8+7y / 64+y^2
f(x, 3) = x+21 / x^2+9
b. Find the partial derivatives at P1
Ans.
fx = ( x^2 + y^2)-(x+7y)2x / (x^2+y^2)^2
fy=(x^2 =y^2)7 – (x+7y)(2y) / (x^2 + y^2)^2
c. Evaluate the partial derivatives at P1
Ans.
fx (8,3) = -391 / 5329
fy(8,3) =337/ 5329
d. Give the equation of the tangent plane through P1
Ans.
f(x,y)= -391x/5329 +337y/5329 +58/73
e. The approximation at P2 obtained from the tangent line
Ans.
f(4,9) = 5703 /5329
Q.4) The function is P1 = (10,-5) , P2 = (2,5)
a. Give the 2 functions of one variable through P1 obtained by holding each variable constant.
Ans.
f(10,y)=100(10+6^y)
f(x, -5) =x^2 (x+6^-5)
b. Find the partial derivatives of the original function.
Ans.
fx(x,y)=x^2+2x(x+6^y)
fy(x,y)=x^2(6^ylogy)
c. Evaluate the partial derivatives at P1
Ans .
fx(10, -5)=5832051944
fy(10, -5)= (25/1944)log6
d. Give the equation of the tangent plane through P1
Ans.
f(x,y)= 583205x / 1944 +25ylog6 / 1944 – 3888025/1944
e. The approximation at P2 obtained from the tangent plane.
Ans.
f(2,5)=250log6-2721615/1944
Q.5) Given the function f(x,y)=x^2+2xy+10y^2+3x-5y
a. Find the partial derivatives of the original function.
Ans.
fx(x,y)= 2x+2y+3
fy(x,y)= 2x+20y+5
fxx= 2
fxy=2, fyy =20
b. Find the critical point in the region.
Ans. The point is (-25/18, -1/9 )
c. Compute the discriminant at the critical point.
Ans. The discriminant is 36.
d. Determine if the critical point is a maxima, minima or saddle point.
Ans. Maxima.
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