Q(2) Let f be a differentiable function whose domain is the set of all real number, and satisfy all of the following conditions: • f (6) = 0 , f'(x) < 0 when z < 6, • f'(x) > 0 whenr >6, • f"(4) = 0, f"(8) = 0, • f"(x)< 0 when I< 4 or z> 8, • f"(x) > 0 for 4

Q: let                    x^2+1   if x is less than 1 f(x)=                   x+1        if x is…

A: Consider the given function fx=x2+1  if x&lt;1x+1   if x≥1. The point is x = 1. Obtain the left hand…

Q: Find the absolute maximum/minimum if any of f (x)=x' +3x² +1 on the interval [-3, 2].

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Q: If ƒ is a differentiable function, find the derivative Y = ƒ(√x) fı x + √√ f(x). 1 ○ y = ƒl (√√x) +…

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Q: 6. Use the nth derivative test to show that -x has a maximum at x = 0.

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Q: Step 4 To find (f-l)'(x) use the theorem that states that if f is differentiable on an interval I…

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Q: If f(q)  = 50 + 50q gives profit when selling q units, and g(t) = t^2 - 12t + 1 gives the quantity…

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Q: Select the true statements regarding a graph of f and its derivatives. □ If f'(c) · ƒ" (c) = 0, then…

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Q: 5. Use the graph of ƒ '(x) shown and the fact that f(2) = 14 to find the value of f(12). f’(x) 8 3…

A: Notice that the graph of f'(x) on 2,8 is a upper semi circle with center (5,0) and radius 3.…

Q: fünction is shown. Which one of the sets of inequalities is satisfied by f and its derivatives at x…

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Q: 3) Suppose that f is a differentiable function with domain [0,5] and f' (3) = 0. True or False: This…

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Q: Sketch the graph of a function that satisfies all the given conditions.

A: We have to sketch a graph satisfying the given condition.

Q: Prove that f(x)=x^3+x-1 has a root in the interval [0,2]

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Q: 4) Find fog, gof , f+g and fg where f (x) = x^2 + 1 and g(x) = x + 2, are functions from R to R

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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: 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: In Problems 9 and 10, find the indicated quantity for y = f(x) =5 – x² and interpret that quantity…

A: Consider the function  f(x)=5−x2

Q: 2. Let f(x) be a function with domain (00, -00) and f'(x) = 2x3+3x²-36r. Find the intervals where…

A: Step 1:Step 2: Step 3: Step 4: