Identify the function which produces the following level curves. 2 1.5 1 0.5 -0.5 -1 -1.5 -2 -2 -1.5 -1 -0.5 0.5 1 1.5 2 O f(o, v) O f(a, u) - + y? – 2 O f(a, v) - a2 +5 +1 O f(o, v) = (a- 1) O None of the others
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- If y is a function of x and the slope of the function is zero at x=10 then to determine that y reaches a minimum dy/dx must be ............... at x=10Find the level curve of the function at c=2 for g(x,y)=(x^3-y)(a) If the function f(x)= x^3+ax^2+bx has the local minimum value -2/9 cube root 9 at x= 1/cube root , what are the values of a and b? (b) Which of the tangent line to the curve in part (a) has the smallest slope?
- Determine S[y] has a local maximum or minimum on the stationary path. (by the value of the O(ϵ2) term in Δ)Q3 Let f (x, y) = 10 xy be defined where 0 < x < 1 and 0 < y < 1 1: Find a formula for the level curve y (x) , defined via f (x, Y) = z, where z > 0 is a constant 2: Are the level curves from problem a) growing or falling ? 3: Are the level curves from problem a) convex or concave ?For each of the following functions, determinewhether the given stationary point corresponds toa local minimum, local maximum, or saddle point: (x, y, z) = x3 + xyz + y2 − 3x (1, 0, 0)