Question 1 (50%) Given a function f(x) = where x ε R. (a) Determine f' (x). (b) Determine f"(x). Find the condition(s) for x under which f(x) is strictly convex.

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: 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: Use the function f(x)=x",x>0 to determine the bigger of the two numbers e' and a

A:

Q: Find the domain and range of the function g(x, y) = x√y

A: Given , gx,y=xyNow , x∈R , y>0 i.e y∈R+∴ Domain .    x,y/x∈R , y∈R+…

Q: A function f(x) = v1 – x² is

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Q: 2 (d) T (x) = Væ + 9Væ7

A: T(x)=x+9x73-2x25Formulaamn=amn1at=a-tddxx=n xn-1

Q: √x² + y² x-1 (a) Find and sketch the domain of f (x, y). 2. Consider the function f (x, y) = 4 (b)…

A: The given function is  f(x,y)= x2 +y2-4x-1 We know that the domain of a function is the set of…

Q: Use the graph of y = f(x) to graph the given function g : g(x) = f(-x)

A:

Q: Let f(x) = 9-5x. Find f(t). f(t) =|

A: given that                                 f(x)=9-5x we have to find f(t). we can find f(t) by…

Q: Q (1): Find fxyz for the function: = xe² + ye* + zey a) f(x, y, z) %3D

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Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

A:

Q: a) Find the local extreme values of the function f(x,y) = 2xy – x² – 2y2 +3x + 4. %3D

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Q: Find and sketch the domain for the following function: g(x, y) = x-y

A: The given function gx, y=4-x2-4y2x-y. We have to find its domain and sketch its graph.

Q: Find the domain of f

A: We have to find the domain of the function: fx=x-2x-6 We know that for any square root function y=fx…

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: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

A:

Q: For the function f(x,y) = ³xy, find fx and fy. fx = (Simplify your answer.)

A:

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

A:

Q: The domain of f(x,y) = /36 – x² – y² is

A: Given: The function in two variables, fx, y=36-x2-y2.

Q: Consider the function y -62 Which of the following statements is true for y? = ze Oy" = 36y…

A: Given,