: Assume f (a, b)→ R is differentiable at some point c E (a, b). Prove that if f'(c) 0, then there crists some > 0, such that f(x) + f(c) for all x (c-8,c+8).

Q: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). Which of the…

A: Given: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). To Find:…

Q: x(x²+3) Q7. Consider the function f : [0, 1] → R, → √√4+24 Explain why (a) f continuous, (b) f is…

A:

Q: Let f be continuous from [0, 1] to [0, 1]. By posing 6(x) = f(x) – x, show that fhas a fixed point…

A:

Q: Define f : R2 → R by letting (y² – x)² (y4 + x²) f(x, y) = if (x, y) # (0, 0), and f(0,0) = 1. ||…

A: The given function is f:ℝ2→ℝ defined as: fx,y=y2-x2y4+x2if x,y≠0,01if x,y=0,0 Claim: The given…

Q: Assume that is differentiable on a ≤ x ≤ b and that f (b) < f (a). Show that f' is negative at some…

A:

Q: Find all differentiable functions f: R→R such that f'(x) = F(x + n) – f(x) n for all real numbers x…

A: As f'(x)=f(x+n)-f(x)n is true for all positive integers values of n thus substitute 1 for n in…

Q: Consider the following function f: R -> R,whose criterion is f(z) = 43x' + 6x – 5 + e9(z) with g a…

A: If you like the solution then please give it a thumbs up.. The Answer is:        f''(a) = 258a + 81…

Q: Consider the function f(x,y,z) = (x+y+z)° on the domain R’. (b) Is f a quasi-concave function? If ƒ…

A: Given: Function f(x, y, z)=x+y+z3 on the domain ℝ3. To determine: Whether the given function is…

Q: Show that the function f defined by (x, y) = (1, –1) f(x, y) = r? + y (x, y) # (1, –1) x + y is not…

A:

Q: Indicate whether the following statement is true or false. Let f(x, y) be any c' real valued…

A: Given fx,y be the C1 real valued function defined on the rectangle R=a,b×c,d. Then we have to check…

Q: Consider the function f(x)=1/x+4. a) As x→−∞, f(x)→ b)As x→∞, f(x)→

A:

Q: Assume that f and g are differentiable functions such that f(0) 2 g(0) and that for all r€R, f'(z) >…

A:

Q: Is there a twice differentiable function f R2R whose best adratic approximation at the point (1,0)…

A: Given problem is from differential calculus in several variables. We have shown that there exists a…

Q: A) If g'(x)>0 for all x in the interval (4,7) then g(x) is for all x on the interval (4,7).| B) If…

A:

Q: Which of the following statements are false? ) The domain of the function f(z, y, z) = + sin-(z + y)…

A:

Q: Assume that f(r, y) is a function given by if (r, y) # (0,0), f(r, y) = 0 if (r, y) = (0, 0).

A:

Q: 1 If the function f is continuous on [a,b], then there exists at least one number C in [a,b] such…

A: If the function f is continuous on [a, b], then there exists at least one number C in [a, b] such…

Q: Let f :-1, 1] -→ R be a three times differentiable function such that f(-1) = 0, f(0) = 0, f(1) = 1…

A:

Q: Suppose that f is differentiable on [a, b]. Prove that if f'(a)f'(b)< 0 then there exists a point c…

A:

Q: (b) Give an example to show that existence of fa(x, y) and fy(r, y) does not imply continuity of…

A: Continuity: A function f is said to be continuous at a point a, b of its domain of definition, if…

Q: be de by 8 <x3 + y3 f(x, y) = x2 + y2 if (x, y) = (0, 0) if (x, y) = (0, 0). %3D (a) Is f continuous…

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

Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: Show that a function f : R2-R defined by f(x,y)= x3- y3 / x2+ y2, if (x,y) is not equal to (0,0)…

A: What is Continuous Function: A function is referred to be continuous at a certain point in its…

Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

A:

Q: (5) Prove that if f is continuously differentiable on [a, b], then |f(a) – f(b)| a – b max f'(x)|…

A:

Q: Suppose that f: R2R is a function given by S x²+y² f(x, y) 0 for xy = 0. Show that f(x, y) is…

A: We have to show the given function  f(x, y) is continuous  at ( 0,0)