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: (x)=3x-2√x I the equation of the secant line through the points (4,f(4)) and (9, f(9)). w that there…

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Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Could you help me solve a problem. Its an explicit formula pertaining to 'Pn=P0(1+r)'n . My equation…

A: Pn = Po(1+r)n 2060=31(1+r)92

Q: Q3) Determine slope of a curve y = x + 2 at p(1,3) and q(3,11)

A: Slope of a curve : The slope of a curve y=f(x) at a point P is the slope of the tangent at that…

Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: What is the slope of the line tangent to the curve √√x + √y = 2 at the point 1 3 (A) -3 (B) (C) 1…

A:

Q: Therefore, the curve y = x* - 2x2 + 2 has horizontal tangents at x-0, 1, and -1

A: Just compute the derivative and equate it to zero.

Q: Which point on the curve y = √x - 4+9 is closest to the point (7, 9)? (x, y) = ( What is this…

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Q: Differentiate the function. r(t) = (3²- + 8)i + r'(t) = (6t)i + ( 132 r'(t) = i + (6t)j r'(t) =…

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Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32

Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: The points at which the graph of the equation 8x2+ y² – 16x + 8y + 8=0 has horizontal tangent lines…

A: