7. Find a and b such that f is differentiable everywhere. f(x) = {+b, S ax³, lx² + b, x< 4 x > 4

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: The function f(x, y) = x² + y² √x² + y² +1-1' (a) {(x, y) = (0,0)} (b) {(x,y) = R²2} 2 if : (x, y) =…

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Q: (x. v) = (0, 0)

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Q: 1. Let h : R → R be some twice-differentiable function. Define f(x,y) =h() for all x ≠ 0. Show that…

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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: A parallelogram is formed by the vectors [1, 2] and [3, -4]. Find the area of the parallelogram. O…

A: Given query is to find the area of parallelogram.

Q: 4. Find the absolute extrema of f(r) = 7r/3 - r7/3 over the interval [-8, 8].

A: Given function is

Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

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Q: 5. Let f be defined for all real numbers and suppose f(x)-f(y)| ≤ (x - y)² for all real numbers, x…

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Q: 8. Show that the function f(2)= 2 is continuous everywhere but not differentiable anywhere.

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Q: 3. Let z = yg(x2 - y²) be a differentiable function. Show that z(x,y) satisfies 1 дz 10z 7 - + - = х…

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Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r - s, s² - 7r). Use the table…

A: ​gr​(7,6)=−50gs​(7,6)=93​Explanation:Step 1:​Given a Table of values of f,g and fx​,fy​​​To find:…

Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: If a and b are real numbers and f(x) and g(x) are differentiable functions such that fla)=g(a)=1,…

A: Introduction: The by parts method is a method to determine integration. When the integrand is given…

Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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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: Determine the interval(s) over which f(x) = (x − 4)³ is concave downward. O a O b Od (-∞0, 4) (-∞,…

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Q: 3. Determine whether f is differentiable or not differentiable at 1. (x – 1 if x > 1 (-x² _if x <1…

A: If a function is differentiable at any point x=a ,then its L.H.D. =R.H.D.

Q: 10. Let F(x, y, z)= y-yz+1 £z+r-z z+xy-y Find a function g such that F = √g.

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Q: Determine if the following functions are analytic or not: 1. f(z) = (z* + 1)³ – 3z* where z is the…

A: (i) The  given function is ;               fz = z*+13 - 3z* We know that a function  f is analytic…

Q: =) Which of the following functions are and /or IZI> 2: हन ii) 2²1 Z-√2+4 analytic in IZK< 2

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Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: 6. Find an equation of the tangent line to y = f(x) : = tan¬(2x) at x = 7

A: Given,

Q: 32. (Refer to the graph of f below) On which interval is f concave upward? y4 y= f(x) -2 6 x 8 -2…

A: The solution are next step

Q: dA XB d(AXB) = Ax dB mp np %3D np Prove that where A and B are differentiable functions of u

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Q: 7. Determine each of the following for the function, f(x, y) = 7x³y² - 2x + 3y. Show all work toward…

A: Given,  f(x,y)=7x3y2-2x+3y