Suppose that f is given for æ in the interval [0, 12] by x = 0 2 468 10 12 f(x) =-13-10|-6-2-1-2-6 A. Estimate f'(2) using the values of f in the table. f'(2) - 1.75 B. For what values of x does f'(x) appear to be positive? (Give your answer as an interval or a list of intervals, eg, (-infinity,8] or (1,5),(7,10) ,) C. For what values of a does f' (x) appear to be negative? (Give your answer as an interval or a list of intervals, eg, (-infinity,8] or (1,5),(7,10) ,)

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A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

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Q: 2. If f(x) = cos2x, find f(0), f(--).f),f(-x) 3. If f(x) = x(x+1), show that f(x+h)– f(x)= h(2x +1+…

A: 2. f(x) = cos2x , find f(0) , f(-π/4), f(7π/8) ,                                         f(-x). f(0)…

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Q: By considering the derivative of the function f: [-1,1] → R defined by f(r) = show r2 +1' that f-1…

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Q: If f'(x) = 3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the local…

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Q: ,x5 (A) 5 (B -4 6 3 (E) none of the given choices

A: Given that, The function f(x) is following, f(x)=x-4,x≤5kx2-24x+46,x>5 We have to find the value…

Q: Suppose the nonzero function f(x) is infinitely differentiable and that f'(x) = -3f(x) for all a…

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Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

A: The objective is to find the derivative.

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Suppose that the values of a smooth functionfis known for x=0, 0.3, 1.2, 1 5 and 1.8. Select the 3…

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Q: For what value of the constant c is the function f continuous on (-∞, 0)? { cx2 + 5x if x 4

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Q: (9) F(<) = { —1, if - п <x<0 1, if 0sxп (h) f(x) — f -х, х, -1<x<0 0<x<1 if if

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Suppose the derivative of f is f'(x) = (x + 1)*(x - 2)*(z- 3). On what interval is f increasing?…

A: A function f(x) is said to be increasing in an interval of it's derivative is positive in that…

Q: Suppose that the values of a smooth functionfis known for x=0, 0.3, 0.6 and 1.2. Select the 3- point…

A: The formula, f'x0=fx0+h-f(x0)h  is known as forward difference formula when h&gt;0 and is known as…

Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

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Q: Suppose that  f is a twice differentiable function (the function has a second derivative…

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Q: 3. Is the function given by (x²-4x-5, x<5 F(x)= x+1, x25 continuous at x = 52 why or why not ?

A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

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Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

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Q: The second derivative of the function g is given by g' (x) = 0.1x³ – 0.29xª – 0.694x³ + 1.9136x². -…

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Q: Suppose that a one-to-one function f has tangent line y=5x+3 at the point . (1,8)Evaluate (f-1)'8

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Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

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Q: We are given that the derivative of f is f′(x)=3x2−12x−15 and that f(1)=81.   The absolute maximum…

A: We are given that the derivative of f is f′(x)=3x2−12x−15 and that f(1)=81.   The absolute maximum…

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Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

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Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

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Q: We are given that the derivative of f is f′(x)=3x^2−12x−15 and that f(1)=81.   local maximum?…

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Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

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Q: * The tangent line to y = f(x) at (-4, 10) passes through the point (-5,-10). Compute the following.…

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Q: Suppose that f and f-1 are both differentiable. Moreover, ƒ(1) = 2, f'(1) = 2, ƒ'(2) = 3. Find the…

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Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.