Consider the function f(x,y) = (3x^2 + bx)(2y^2+dy) where b and d are non-zero constants. Determine the values of b and d so that point (3,1) is a saddle point of f and calculate the value of b + d.

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: Find the points on the curve y=x(x-1)(x-2) which have the same gradient use @ for 2

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Q: Estimate f(2.98, –1.99) given that f(3, –2) = 2, f«(3, –2) -3 and fy(3, –2) = -4. = f(2.98, –1.99)

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Q: Evaluate W(3,-1) for the function W(x,y) = 4x^2 + y^2

A: W(x,y) = 4x2 + y2Find W(3,-1)

Q: Graph the function along with secant lines AP, BP, CP where A = (0, 9) B= (1,7) C = (1.5,4.5) P =…

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Q: Question 3.5: Calculate o dz. Question 3.6: Calculate o 1 - dz .

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Q: Determine the relative extremes of F (X, Y) = 5X ^ 2 + 6Y ^ 2-XY if X + 2Y = 24

A: Given function is FX,Y=5X2+6Y2−XY and X+2Y=24. We have to find the relative extremes of the given…

Q: Find domain and range of the * function y = Vx2 – 4x

A: To find the domain and range of  y=√(x²-4x)

Q: What is the fxx, fyy, and fxy of f=(2x^4)+(y^2)-(x^2)-(2y)?

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Q: Find the slope of the curve f(x)= x2 at the point P(2,4)

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Q: Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every…

A: integration

Q: Choose the point that corresponds to t=-1 when x=t^2-4 and y=t+1/t (-3, 0) (-3, -2) (3, 2) (-5,…

A: Given,x=t2-4andy=t+1tat t=-1x=-12-4x=1-4x=-3andy=-1+1-1y=-1-1y=-2