ppose that f is a continuous function and the followi ƒ(2) = 2, ƒ(4) = −1, ƒ(6) = 6, ƒ(8) = = culate F'(2). 21 -32 -10 4x F(x) = [₁² f f(t) dt.

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

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Q: (a) f(x) = F(x, 2): then ƒ'(x) = (b) f(x) = F(4,x): then f'(x) = (c) ƒ(x) = F(x,x): then ƒ'(x) = (d)…

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Q: If f(x) is continuous on (-15,-5)such that, -10 SI5 f(x)dx=13 and/" f(x)dx =6 then find f(x)dx -10…

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Q: Let h = fog where ƒ : R² → R and g: R² R² is defined by g(x, y) = (3x²y, x – 2y). Find the…

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Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

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A: Given F(u,v)be a function of two variables. let Fu(u,v)=G(u,v) and Fv(u,v)=H(u,v) Here f(x)=F(u,v)…

Q: af Suppose f = f(x, y) and let |(0,5)= 2 and |(0,5) = 8. 3x Define the function g(t) = f(tº - t,…

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Q: Suppose that f'(x) = 2x for all x. a) Find f(4) if f(0) = 0. b) Find f(4) if f(2)= -1. c) Find f(4)…

A: Given f'( x ) = 2x

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: The derivative of the function f(x) = elan(=) + Ve is

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Q: (20p) Let f be a differentiable function satisfying the equation f(a + b) = f(a) + f(b) + 2ab for…

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Q: Find and interpret f'( – 2) and f''(– 2). 3 f(x) =

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Q: The acceleration of a particle as it moves along a straight line is given by a-21 -1. Ifs 1 and y- 2…

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Q: Let f (x) 6x + 3 Then the derivative of f is 2х— 1 Ax + B f'(x) where (2x – 1)C' %3D B = C = || ||…

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Q: 8 f'(t) dt 24, what is the value of f(8)? If f(3) 12,f is continuous, and 3

A: Given,

Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

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Q: Suppose f(x) = 6t²√1+tº dt. 1) Evaluate f (2). 2) Evaluate f'(2). 3) Evaluate f"(2).

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Q: let p(x)=g(f(x)). use the given table to find p'4

A: p(x)=g[f(x)] diff. w. r. to x p'(x)=g'[f(x)] . f'(x)  ..................(1)

Q: The interval in which the function f(x) = 2x – 12x is decreasing is O a. (-0,0) O b. (-0,-4) O c.…

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Q: A function f(x) has an inflection point at (1,8). Which of the following could have been the result…

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Q: The function(x)= is concave down on which interval?

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Q: Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8,…

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Q: Let f and g be functions differentiable on R. with Find f(x)|x=2= d g(2) = 2, 9(x)\x=2 = 4, de…

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Q: 3. Suppose that f is differentiable on all of R and g(x) = f(x)². If the table below describes the…

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Q: Differentiate the function. P'(W) = P(w) = 6w² - 4w+2 √w W

A: To differentiate the following function.