a) Find the extreme values of f(x, y) = x' + y' - 3xy +1 by using the Second Derivatives Test. b) Find the extreme values of ƒ(x,y)=2x² + y² on the circle x² + y² =1 by using the Lagrange Multipliers.

Q: the line (x/a)+(y/b)=1 moves in such a way that (1/a\power{2})+(1/b\power{2})=(1/c\power{2}) ,where…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

A:

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A: y = 2 + 3x - x3    => y' = dy/dx = 3 - 3x2 = 0 (set)                => 3(1 - x2) = 0…

Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

A:

Q: The point P(5,-2) lies on the curve y = (a) If Q is the point (x, (1) 4.9 MpQ (ii) 4.99 MpQ (iii)…

A: Given that P(5,-2) and y=24-x the equation of the curve. Q (x, 24-x) lie on the curve.

Q: 1) y%= (ans.: max.(1,0.5); min.(-1,-0.5)) 1+ x in (2 3-50,8))

A:

Q: The equation of the tangent line to the curke x? + y = 36, at (6,-16) is %3D y = (x+6) + 16 16 16 16…

A: we have to find the equation of the tangent line to the given curve at (6, -16)

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax ) then,…

A: Both approximation is second order O((∆x)^2)

Q: (a) y = 3x-1 (b) x² + y² = 1 (c) y = sin(x)

A:

Q: If the time 26 + 1%/16 = 1 a that moves in such a way b 1/2 + 1/2 = 1/², where c is a constant, they…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

A:

Q: Find f(X) if F(0)=0 and the tangent line at (x,f(x)) has a slope X(x^2+2)^3

A:

Q: 3. If f is the function given by f(x) = -x³ + x² + 3x-2, name the open interval where the graph of f…

A:

Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: If y=f(x) be the curve that lies on the xy plane, then its length from x=a to x=b is given by…

Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

A: