Let f(x)be a function on (0, o0) satisfying the following: f(x) > 0 on the interval (0, ) f'(x) > 0 on the interval (3, 8) f'(x) < 0 on the intervals (0, 3) and (8, co) f"(x) > 0 on the intervals (0, 3) and (8, ∞) f" (x) < 0 on the interval (3, 8) • f(x) is differentiable at x = 8 Mark all the correct statements. Note: There are exactly four correct statement. Each wrong statement will delete out a correct one. Türkçesi: f(x), (0, 0) aralığında tanımlı aşağıdakileri sağlayan bir fonksiyon olsun. (0, 00) üzerinde f(x) > 0, (3,8) üzerinde f'(x) > 0, • (0, 3) ve (8, ∞) üzerinde f'(x) < 0, • (0, 3) ve (8, 0) üzerinde f" (x) > 0, • (3, 8) üzerinde f"(x) < 0, • f(x), x = 8 de diferansiyellenebilirdir. Doğru olan bütün şıkları işaretleyin Not: Tam olarak dört tane doğru şık vardır. İşaretlenen her bir yanlış şık işaretlenen doğru bir şıkkı silecektir (götürecektir). Lütfen bir ya da daha fazlasını seçin: O (8,f(8) ) is an inflection point of f ( (8,f(8) ), f in büküm noktasıdır) O fis increasing on (0,3) and (8,00) ((0,3) ve (8,00) aralıklarında f artandır) O fis concave down on (0,3) ((0,3) aralığında f aşağı konkavdır) O fis concave up on (0,3) ((0,3) aralığında f yukarı konkav) O (3,f(3) ) is an inflection point of f (3,f(3) ), f in büküm noktasıdır.) O fis increasing on (3,8) ( (3,8) aralığında f artandır) O fis concave down on (3,8)( (3,8) aralığında f aşağı konkavdır) O fis concave up on (3,8) ( (3,8) aralığında f yukarı konkav)

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: Let f(æ) = In a*(x + 5)*(2² + 4)*| f'(x) =

A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

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Q: Suppose that f (0) = 2 and f'(x) 0. Show that f(4) 0.

A: f(0)=2   and f'(x)≤3  for all x&gt;0 ⋯(i)integrate (i) w.r.to x ,we getf(x)≤3x+kput…

Q: 9) Sketch the graph of a function f(x) on the interval (-4,4) with the following properties. f(x) is…

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Q: Sketch the graph of f(x) if ...f'(x)&gt;0 on (2,4) and f'(x)&lt;0 on (−∞, 2) ∪ (4, ∞),f''(x)&gt;0 on…

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

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Let f(x)be a function on (0, 0) satisfying the following: f(x) > 0 on the interval (0, o0) f'(x) > 0…

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Q: Let/be differentiable for all x, lff(1) = - 2 and f'(x) 22 for all xe (1, 6), then find the range of…

A: f(1)=-2  f'(x)&gt;=2  for 1&lt;x&lt;6

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Q: 1’) Let f be the function f(x) = x^2 +36/x^2 (a) Calculate f'(x) and find all stationary points for…

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Q: Sketch the graph of a single function that has all of the properties listed.

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Q: Find f such that f'(x)=x²-4 and f(0) = 5. f(x) = 0

A: f'x=x2-4

Q: Sketch a graph of the function that satisfies all of the given condition. f'(1) = f'(-1) = 0, f'(x)…

A: f'(1)= f'(-1) =0 When derivative is 0 then there will be maximum or minimum at x=1  and x=-1…

Q: Find a function f that satisfies the conditions. f"(x) = x-3/2, f'(1) = 4, f(4) = -2 f(x) =

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Q: Let f' (x) 0 for all x with -o∞ f(c) More information is needed.

A: Given  Let f'x&lt;0 and f''x&gt;0 for all x with -∞&lt;x&lt;∞ Let a,fa and  c,fc be two points on…

Q: Given f'(x) = 4x³ + 12x², determine the interval(s) on which f is both increasing and concave up,…

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Q: Let f(x) = 5x² cos(2x). f'(x) = -10x²(2x) + 10x cos(2x) f'(5) = 0 f"(x) = -10x² sin (2x) + 10x…

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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: Consider f, a function such as f(2) = 1, f'(2) = 2, f''(2) = 3 and f'''(2) = 4 and that verifies:…

A: Given: f(2)=1, f'(2)=2, f''(2)=3 and f'''(2)=4 To find: Error bound in the approximation of f1.

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Q: Suppose that f and g are functions such that (0) = 4, f'(0) = 5, g(0) = –2, gʻ(0) = 3. %3D æf(x)…

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Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

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Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'…

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Q: Let f(x)be a function on (0, o) satisfying the following: f(x) > 0 on the interval (0, o0) f'(x) > 0…

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Q: Find f such that f'(x)=x² +4 and f(0) = 1. f(x) =

A: NOTE: Refresh your page if you can't see any equations. . take integration on both sides

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Q: A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven,…

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Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.