Let f mapping R into R be a function, and let X be a subset of R2. (a) Define what it means for f to be convex. (b) Define what it means for X to be convex. (c) Define epi(f) = {(x,y)|y>=f(x)}. Describe the relationship between epi(f) and the graph of y = f(x) in R2. (d) Prove that if epi(f) is a convex set, then f is a convex function.

Q: Sketch the level curves of the function f(x, y) = y² for c = -4,-1,0, 1, 4. ²5 T

A: Given that the function is                           To sketch the level curves of the given…

Q: f(x,v) x2

A:

Q: Consider the function of two variables defined by: f(x,y) = (x3y4) / (x-7210)2+(y-9245)2 What…

A:

Q: Sketch the level curves of the function z(x, y) = 10- 9 8 7 6 5 4 3 -10 -9 -8 -7 -6 -4-3-2 2 4 5 6 8…

A: Level curves equation   y=-6x/5Explanation:

Q: Explain how the graph of f can be obtained from the graph of y=(1)/(x). Then graph f. A) The graph…

A: Concept,When we shift the graph to the right we subtract the value from x.When we shift the graph to…

Q: Sketch a contour map of the function. f(x, y) = x² +9y² y Q Sketch the graph of the function and…

A:

Q: Let f(x, y) = √√/175 – 3x² – 4y² Evaluate f(1,4)

A: Given :To Find :

Q: f(x, y) = [x² + y² if x² + y² < 1 1 if x² + y² ≥ 1

A:

Q: Consider the function f : R2 → R, (x, y) → √25-x² − y². (a) State and sketch the level curves for f…

A:

Q: Consider the function f(x) = ao + a₁x + a₂x² + a3x³ + a²x¹. The goal of this exercises is to find…

A:

Q: describe the function's level curves, (d) find the boundary of the function's domain, Q2: (a) Sketch…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Sketch the level curves of the function f(x, y) = = - y² for c= -4,-1, 0, 1, 4. 9

A: The level curves of a function f(x,y) are formed by plotting points (x,y) in the plane where f(x,y)…