Consider the function a) b) Prove function & R R given by Prove there that Prove f'(e) f(x) there exists exists 3x³ 3x²² -3 c € (0₁²) there exists f' (d) = 0 12. r f(c) = 0. Such that d E (0,1) Such et (1, 2) such that that

Q: If f(a) = 7 and f(b) = 0, then there exists a number c in the interval (a, b) such that f'(c) 7 a –…

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Q: 2+x 5. Given f(x) =<tX Find X-4 %3D a) fe) b) f(a+1) c) f(x) + f(h)

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Q: 5) if it is r = √ x² + y² + Z² and fir) a deritable function prove that √ ² f(r) = d²f then find…

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Q: 3) Given the function f(x) defined by the table below, 1 4 2 8 b) a) Evaluate f(6) Solve f(x) = 4 c)…

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Q: Theorem: Let f,g € C(X)are continuous function then 1) f + g is continuous function and (f + g)(x) =…

A: To prove the given statements.

Q: 3, 5x 60(x 2 + x;), 3 b) Y = In 7.

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Q: If f'(x)=0 for all *, then a) f(x)=(x) for every x₁ x₂ c) f(x)>(x) for every x₁>x₂ d) f(x)>(x) for…

A: If  then which option is correct .

Q: if f(z) analytic in |z| 2? f(z) = (z2 -1)/(z - sqrt(z2 + 4))

A: Given fz=z2-1z-z2+4fz=z2-1z-z2+4×z-z2+4z+z2+4fz=z2-1z-z2+4z2-z2-4fz=z2-1z-z2+4-4 So,…

Q: Let f: X → Y and g: Y → V be functions. Show the following: (a) f is injective 3h : Y→ X such that…

A: Given Data: Let f:X→Y and g : Y→V be functions.To Show that,(a) f is injective ⇔∃h :Y→X  such that h…

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: 1 is IR? \ {(0,0)}. 22 + y2 The domain of the function f(*, y) True O False

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Q: 9. Find bijective functions from R to R a) f (x) = 2x + 1 b) f(x) = x² + 1 c) f (x) = x³ %3D x2+1 d)…

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: Find continuous functions f1, f2, f3, f4 defined on the open unit interval I = (0, 1) (i.e.…

A: 1. f1(x) = (M1 - L1)x + L1, for all x in (0, 1)  This function is linear and maps (0, 1) onto (L1,…

Q: What is true about the function f(x)= = a) f(x) → from above b) f(x) →2 from above c) f(x) → from…

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Q: What is the range of the function f(x) = = x + b -, a, b = R and a, b =0? xa

A: range of fx=x+bx-a

Q: 7) Let f(x) be a function such that f(1) x E [1,6]. Find how small can f (6) possibly be? Explain.…

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Q: a) f(x,y) = x³ + y³ + y(3x²y+ 3ry²) b) f(x,y) = x² + iy³

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Q: Let /: X→Y be a function, A, B C X and C, DCY. Show that: 3. If CSD then SF (D) 4. f¹(COD)=f-¹(C)…

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Q: x3 +x2 3 Prove that if f (x) then f"(x) = – x² Find g'(x) and g"(x) if g(x) = (2x – 3)² (x + 4)³. 2…

A: Ans (1). Given that, f(x) = x3+x2-12x2 f(x) = x + 1 - 12x2 now differentiate the function, f'(x) = 1…

Q: for If f (2) is a regular function of z, prove that f (2) 2 = 4 | f'(2) 1?. %3D ve I f12) 1? =4 |…

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Q: • Let a) f: IR₁ ->R₂ & f(x) = - = b.) f: IR₁ → IR₂ & f(x) = 2x² +7 EXC 3X 3 2 Do some appropriate…

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Q: State the interval of the function g(x) = E-x is %3D

A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: Express the function h(x) f(x) ‡ x and g(x) ‡ x. a) g(x) = = X 1 x - 1 in the form h(x) = = b) f(x)…

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Q: 3 prove that sinh (2) isine

A: Since you have posted multiple questions, we will provide the  solution   only to the first question…

Q: show the function is continous dis continou or 2=(2x+3 3メ→1」Xハz F(x)ニ

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: b) Euler's theorem states that f(:) = "/ax, · ×1 +°' /ax, ' x2 for functions that are homogenous of…

A: The given function is: f(x1,x2)=x12+x22 Now, to verify: f=∂f∂x1x1+∂f∂x2x2

Q: For questions 8-10, let f(x) be a function defined everywhere such that f"(x) = 3x² – 12x. What are…

A: Definition used -                   Point of inflection - A point where the concavity of graph of…

Q: Does there exist a function f such that f(0) = -9, f(2) = 9, and f'(x) 5 7 for all x? O Yes O No

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Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution: