Suppose that f(a, b) is an absolute maximum of the function f (x, y). Must f (a, b) also be a local maximum of f (x,y)?

Q: find the maxim um anel minimum Limits of the functibu :- Fixy) = x"; + y- 2x-4xy-2y?

A:

Q: Find the maximum of y = xa − xb on [0, 1], where 0 < a < b. In particular, find the maximum of…

A:

Q: Determine whether the following statement is true or false, and explain why. For a function z = ƒ(x,…

A: Let f(x, y) and its first and second derivatives are continuous at (a, b) and that fxa, b=fya, b=0,…

Q: Say if the following statement is true or false: If a function f is twice differentiable at the…

A: If c is a critical point of the function, then  f'c=0. To check whether the critical point…

Q: Suppose that f(x, y) = 5x + 2y at which - 4 < x < 4, – 4 < y < 4. %3D Absolute minimum of f(x, y) is…

A:

Q: Suppose that f(x, y) = x² − xy + y² − 5x + 5y with z² + y² ≤ 25. 1. Absolute minimum of f(x, y) is…

A: Given function is fx,y=x2−xy+y2−5x+5y subject to x2+y2≤25. We have to find the absolute minimum and…

Q: Show that the limit of the function f(x,y)= (0,0). (x+y)² x² + y² is indeterminate at

A: Limit of the function

Q: If f, (a,b) = f, (a,b) = 0, does it follow that f has a local maximum or local minimum at (a,b)?…

A: Given, fx(a,b)=fy(a,b)=0

Q: Provide an appropriate response. Given that x > 0, find the maximum value, if any, of x-x".

A: Given that x&gt;0. We have to find the maximum value of  x1x5.

Q: Suppose that f(x, y) = 5x + 2y at which -4 < * < 4, – 4< y < 4. Absolute minimum of f(x, y) is -28…

A:

Q: Let f(x, y) = g(x) + h(y) where g(x) and h(y) are positive. If g(xo) > g(x)and h(yo) > h(y) then…

A:

Q: Let f(x) be a differentiable function. Explain why it is possible that f'(c)=0 for a function but…

A: Let f(x) be a differentiable function.

Q: Determine whether the following statement is true or false. If f'(c) = 0, then f has a relative…

A: To determine true or false.

Q: Determine whether the statement "If f has a relative maximum at (x0, y0, z0), then fx(x0, y0) =…

A: Statement: If f has a relative maximum at (x0, y0, z0), then fxx0, y0=fyx0, y0=0. The above…

Q: How do I solve this?

A: Global maxima or minima of f(x) in [a, b] is basically the greatest or least value of f(x) in [a,…

Q: Give an example that: the f'(c) 0 but c is not a local maximum or local minimum.

A:

Q: Suppose that f(æ, y) = x² – xy+ y² – 5æ + 5y with æ² + y² < 5?. 1. Absolute minimum of f(x, y) is 2.…

A:

Q: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: Consider the function f(x) = z over the interval (-2, 2). Does the extreme value theorem guarantee…

A:

Q: Let f(x) be maximum and g(x) be minimum of {x|×|, x² | × [} then

A: 9

Q: Let f(x) be maximum and g(x) be minimum of {x|×|, x² |x} then

A:

Q: By choosing x, find a maximum of xre-x, if r>2, otherwise the function goes to infinity at x=0.

A:

Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: Find the global maximum and global minimum of f(x)=2x in the interval [−1,3].

A: Given function is Differentiating with respect to x, we get Now, f'(x) =0 for no value of x and…

Q: Suppose that u(x) is a differentiable function such that

A:

Q: 2. Suppose that f (a, b) is an absolute maximum of the function f(x, y). Must f (a, b) also be a…

A:

Q: If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f'(0) and…

A:

Q: Suppose that f(x, y, z) = 4x + 4y + 3z at which 0 < x, y, z < 5. 1. Absolute minimum of f(x, y, z)…

A: We have to find the absolute minima and maxima.

Q: Suppose that f(x, y) = x² + y at which 0 < x, y and 3x + 9y < 7. 1. Absolute minimum of f(x, y) is…

A:

Q: Let f(x, y) = g(x) + h(y) where g(x) and h(y) are positive. If g(xo) ≥ g(x)and h(yo) ≥ h(y) then…

A: Thus the given FIRST statement is TRUE.

Q: Suppose that f(x, y) = x' + y – 2xy Then the minimum is

A: Solution is given below:

Q: Suppose that f(x, y) = 5x + 2y at which – 4 < x < 4, – 4 < y < 4. %3! Absolute minimum of f(x, y) is…

A:

Q: -- ) Determine the values of constanas a, b, c, and d so that f(x) = ax³ + bx² + cx+d has a local…

A: As given (0, 0) is a point of local maximum and (1,−1) is a point of local minimum of f(x). The…

Q: Find the absolute maximum of f(x,y) = 5x²y² + 4y² + 6x² bounded by y = x, y = 0 and x = 4. %3D…

A: The given function is: f(x,y)=5x2y2+4y2+6x2Bounded Region is:  y=x,  y=0,  x=4

Q: What is the absolute maximum value of the function f(x, y) = e¯z²-v² +1 (x² + 4y²) on the closet…

A:

Q: Estimate the global maximum value for the function F on the interval [-2,1] if F(x)= || dt . t2 +1

A: The given function is: F(x)=∫-2x tt2+1 dt

Q: Determine the values of constanas a,b,c, and d so that f(x) = ax^3 +bx^2+cx+d has a local maximum at…

A: Given that f(x) = ax3 +bx2 + cx + d has a local maximum at the point (0,0) and a local minimum at…

Q: If x = c is in the domain of f such that f'(c) = 0 and f"(c) > 0, then f has a local maximum at x=…

A: The given problem is solved below in detail.

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given function is fx,y=x2+y2.…

Q: Find the absolute maximum of f(x,y) = 3x²y² + 5y2 + 5x² bounded by y = x, y = 0 and x = 1. Answer:

A: Solve the above problem.

Q: What are the absolute maximums and minimums of z(x) over its domain?

A: Given To find what are the absolute maximums and minimums of z(x) over its domain.

Q: What is the local minimum value of the function f(x) = x^3(x + 4)

A: We have the given function as fx=x3x+4 For local maxima/minima, we need to calculate critical point…

Q: (b) Sketch the graph of a function that has a local maximum at 3 and is continuous but not…

A: To sketch the graph of the function which is local maxima at 3 and not differentiable at 3

Q: True False  Suppose f(x) satisfies f'(3) = 0 and f"(3)&gt;0, then f(3) must be a local minimum.

A: We will use the second derivative test to answer this. It states that if, at a point x = c, the…

Q: Suppose that f(x, y) = x* + y* – 2xy Then the minimum is

A:

Q: Let f(x, y) = g(x) + h(y) where g(x) and h(y) are positive. If g(x₁) ≥ g(x)and h(yo) ≥ h(y) then…

A: