A. (a) Sketch the graph of the function given (b) Determine if it is continuous at x, (c) Identify that f'-(x1) and f'+(x,) if they exist

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

Q: Provide an example of a function f(x) which has all of the following properties: - it is periodic…

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Q: 4. Consider the function g(x) = r+3° a) Find the derivative of g using differentiation rules. b)…

A: The given function, g(x)=2x+3

Q: Let f(x) = x6, x ≤ 1 √√x, x > 1 Determine whether f is differentiable at x = 1. If so, find the…

A: Given :fx=x6,x≤1x6,x>1to check differentiable at x=1

Q: 5a) Using the formula man = lim+)=/G2 determine the derivative/ slope of tangent for h→0 the given…

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Q: Suppose that a function ƒ satisfies the following conditions for all real values of x and y: i) ƒ(x…

A: The given conditions are,

Q: 5. Use the definition of the derivative to find f'(x) if f(x)== x-÷ (i.e. ƒ(x)= . (i.e. f(x +h)-…

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Q: The definition of the first derivative of a function f(x) is: Select one: f(x+Ax)-f(x) a. f'(x) =…

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Q: Consider the function f(x) = V1 – 5x. a. Use the \underline{limit definition of derivative} to find…

A: We have to find the following given condition

Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: 4. Consider the function g(x) = I +3 a) Find the derivative of g using differentiation rules. b)…

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Q: Let a be a real valued constant. Find the derivative with respect to x for the function f (x) =…

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Q: Define the derivative f'(a) of a function f at x =a.

A: To define: The derivative f'(a) of a function f(x) at x=a

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given: fx=xnsinx

Q: The limit cos(x) – 1 lim с — 4т represents the derivative of some function f (x) at some number a.…

A: This question is about finding derivative about a point .

Q: Let f(x) be a function that is differentiable at x = -2. Given that f'(-2) = 3 and f(-2) = 6, find…

A: Given data: f'(-2) = 3 x1 = -2 f(-2) = y1 y1 = 6

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: fx=cosxxn When n=1, fx=cosxx Differentiating with respect to x, we get…

Q: 2. Let f : R → R be a differentiable function. Show that the function f', the derivative function of…

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Q: 1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >1…

A: A function f is said to be continuous at a point x=a if limx→af(x)=f(a).  The left hand derivative…

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

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Q: 3. Sketch the graph of a function that is continuous, but not differentiable at I= 1.

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Q: Consider the function f(x) = x2 - 1. (a) Find f '(x) using the limit defination of the derivative.…

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Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: The limit represents the derivative of some function f at some number a. State such an f and a. 16 +…

A: This question is about differentiation expressed as limit of a function

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

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Q: 5. Use the limit definition of the derivative to find the derivative of f(x) = 3x-2. f(x+h) - f(x)…

A: f'(x)=limh→0 f(x+h)-f(x)h

Q: [8] Use the definition f(a +h) – f(a) f'(a) = lim h-0 h To find the derivative of the given function…

A: Given: So,          f'(2)=limh→0f(2+h)-f(2)h       =limh→ 012+h-12h       =limh→ 0-12h+2       Plug…

Q: 1. Let f(x) = Find the equation of the tangent line to the graph of f'(x) at the point x² + 1 where…

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Q: The limit x°-1 lim x→1 r - 1 represents the derivative of some function f(x) at some number a. Find…

A: We need to find f(x) and value of a.

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x sin x n = 1 f'(x) n = 2…

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Q: The first derivative of a continuous function y=f(x) is given, find y’’ and then sketch the general…

A: Our objective is to find y'', and then sketch the general shape of the graph of  f.

Q: The graph shown represents the graph of THE DERIVATIVE ƒ' (x) of an unknown continuous function…

A: Given, Graph of the f'(x) is shown as:

Q: 6. Suppose that f(x) = g(y) + x²y³ r + y (a) Use implicit differentiation to compute a formula for y…

A: We differentiate above function with respect to x and f(x) and  g(x) are function of x and y

Q: This limit represents the derivative of some function V16+h-2 f at some number a. State this f and…

A: Given limit as a derivative of the function limh→0(16+h)14-2h  we have to find the value of a and…

Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

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Q: Consider a function f continuous and differentiable on R with f(2. 5) = -3. 1 and f'(2. 5)=-0. 2.…

A: We have to find

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x" sin x n = 1 f'(x) n = 2…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given:fx=cos xxn for n=1,2,3,4Formula:ddxuv=vu'-uv'v2

Q: Let be a differentiable function such that f(3)=2.345 and f'(x)= ln(x^2+1).What is the value of…

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Q: The graph of derivation function g(x) for a differentiable function g(x) over R is given below and…

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Q: 4. The graph of f'(x), the derivative of a function f(x), is shown at right. Which of the following…

A: f(x) is continous at x=a f(x) is also differentiable as f'(x) exists at x=a ; Since f'(a) is not  0…

Q: Suppose g is a continuous function on the interval (-5, 4). The graph of g', the derivative of g, is…

A: Suppose g be the continuous function and g' be the derivative of the function g. Critical point: The…

Q: Sketch the graph of a twice-differentiable function y = f(x) that passes through the points (-2, 2),…

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Q: 1 Let f(x) X - 1 (a) Find the derivative f 'of f. 1 f '(x) = (x – 1) X* (b) Find an equation of the…

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Q: Consider the function defined by f (x) = -x + ae" where a E R: (1) find a such that the graph of the…

A: To Determine: Consider the function defined by f(x)=-x+aex-1 where a∈ℝ find a such that the graph of…

Q: Let (a) Show that f(x) is differentiable and that the derivative f(x) is continuous.

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Q: Consider the function y = g(x)= -x² + 3x +2. Compute g(2). Use the limit definition of the…

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Q: 2. Let x² sin () if x + 0 g(x) = if x = 0. Is g differentiable at 0? If so, find g'(0). Justify your…

A: Given: gx=x2 sin1x,       if x≠00,     if x=0 To Find: Is g differentiable at x=0? If so, to find…

Q: (a) Give an example of a function f that is differentiable at 0 but whose derivative f' is not…

A: Darboux theorem: Let, f is differentiable functions on [a, b] then for every k with…