Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx², c < 0

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: 2. Check the following function f(z) = iz – 3z is analytic or not (Use C.R equations).

A:

Q: a) Consider the function f (x, y) VIn (4 – x² – y²). Find the domain - and range of f(x, y).

A: Solution is given below..

Q: Consider two functions, f: R2 → R and g: R² → R, such that. • fis C² 2 4.5 = [33] ● g is defined by…

A: f:ℝ2→ℝ and g: ℝ2→ℝ f is C2 Hf4,5=2-1-13 g is defined by gx,y=fx-y,yx

Q: c) f (x) = v9 – 3x

A: See the solution below.

Q: 3. Determine the domain of the following function, then sketch it: 1 f(x, y) = V² + y? – 9

A:

Q: Evaluate the following functions. 1. Iff(x) = x? - 2x +7, find a) f(0), b) f(2y+1). 2. If F(y) = vty…

A: Given:1. fx=x2-2x+72. Fy=yy-32

Q: 1. Given the function S(a) = Find (a) all the a and y-intercepts,

A: The solution is given below in the next step: Also in step 3 graph is provided for better…

Q: 4. Consider the function Check whether f is concave, convex or neither. f(x, y) = x² - y² + 2xy + 2x…

A: Please find attachment for the details solution

Q: If y =f (x) is a function in x then prove that f(a + nh) ="C,f(a) +"C, Aƒ(a) +"C,ƒ(@) + +"C, A"…

A: Given: y=fx is a function in x Prove that: f(a+nh)=C0nfa+C1n∆fa+C2n∆2fa+…+Cnn∆nfa…

Q: Find the local extrema points of the function f(x)=(x−a)ex, where a is an arbitrary real number.

A: Consider the function

Q: 1. Given that f is the function defined by f(x, y) = 2¹+y²-²-2y, determine the relative extrema of f…

A:

Q: Consider f(x) = 3|x|, which is in R[-2, 2]. %3D b. Use the function F(x) to find ſ², f.

A:

Q: If the function f: R\{2} → R\{2} defined by f (x) = 2х+3 then the composite function х-2 fof (x) =.…

A: Use the definition of composite function f∘gx=fgx, to obtain f∘fx. fx=2x+3x-2f∘fx=ffx=f2x+3x-2

Q: Find all local extrema of the function f given by f : R? → R, f(x1, r2) = 3x7x2+ x} – 3a? – 3x3 + 2.

A:

Q: 2. Check the following function f(z) = iz – 3z is analytic or not (Use C.R equations).

A:

Q: 4. For the functions f(x) = Vx -3 and g(x) = Vx+2, find and detemine the domain in ease case. a. gf…

A:

Q: Consider the table of values for the function f(x). X 1 2 W|N 3 4 a) 3 b) 4 O c) 1 y = f(x) 3 1 What…

A: Given query is to find individual function.

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: Let f(x) = 5- x and g(x) 2, find: a. (fog)(0) b. (go f)(0) = c. (fo g)(x) Preview d. (go f)(x) =…

A: Value of the above ques is

Q: 5. Assume that V × F = V × G. What is the most general relationship between F and G ?

A: ∇ x F = ∇x G =&gt; ∇ x (F - G) = 0

Q: 3) Show that f = f, ху for the following function: ху (x° у) f(x. y) + In(x° + y30 ) 20

A: We have to prove that fxy = fyx

Q: Let the function f(x) be given as follows: ax + b, x<1 f(x) = ; lt +x + 1, x 21 Employ appropriate…

A: is differentiable. Therefore, we have, RHD=LHD=f(x) Now,

Q: H.W: Determine which the following functions are differentiable. a) f(z) ix ze.e 6) f(Z) =

A: Let us consider the complex function f(z)=u+iv then the function is differentiable if and only if…

Q: 2. Check the following function f(z) = iz – 37 is analytic or not (Use C.R equations).

A:

Q: Consider the functions f (x) = Vx – 4 and g(x) = Vx – 4, are their domains the same or different?…

A: Find the domains of the given function