Consider the continuous function h with h' (x) = ln(x2)+4/2x1/2 3.1 Find and represent the domain of the function, using set notation. 3.2 Use a number line and the first derivative test to identify the local extreme(s) of the function h by giving the exact x-value(s) of the local extreme(s).

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

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Q: 36x – 270x + 4. Differentiate r and use the Consider the function r(x): derivative to determine each…

A: Solve the following

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A: (a) Consider the function f(x)=-7x3+21x+3 to find the critical numbers of f, set the first…

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A: solution is here

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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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A: follow next step

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A: Now differentiating with respect to x, we get

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A: We have to find the following given condition

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Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: 4. Find the local maximum and minimum values of f, using both the First and the Second Derivative…

A: The given function is fx=x2x-1. Compute the critical points as follows.…

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A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: Find the critical points of f(x) = sin2(x) – cos(x) in the interval (-x, x) and apply the Second…

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Q: 2) Given: f(x) = x+sin(2x) over the interval (0,7) a) Use a sign analysis to find the relative…

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Q: The derivative with respect to x of the function y = 3tan ¹x - y' = cotx O the above (In 3) log3…

A: Given y=3tan-1x-ln3log3cosecx

Q: Given the graph of derivative f'(x), find: a) Any interval(s) where f(x) is decreasing b) Any…

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Q: 4. Consider the function f(x) = Vx – 1 (a) Use the limit definition of derivative to find f'(x)

A: Ans:- Consider the function f(x)=x-1(a) we have to use the limit definition of derivative to find…

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Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >…

A: the given function is: fx=px+1     if  x≥1x2+p      if  x<1 we have to show that the given…

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: Consider a function f with domain {x|x + 0} and the following derivatives: 2 bx3 bx² – 1 bx? f' (x)…

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Q: 4. Given the function f(x) = Vx – 4, use the definition f (x) f(x + h) – f(x) lim h →0 to h (a) find…

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Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

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Q: 2.) f(x) = (x5 – 2x³ + 1) 3

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Q: 2.) f (x) %3D х

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Q: We want to study the following function on the interval I = [−2; + ∞[ g(x) = 3x2+4x+3/x2+1 a)…

A: Given: g(x)=3x2+4x+3x2+1  To find: a) Derivative and critical point of g. b) limx→+∞g(x) c)…

Q: Use y = (x2 – 6x)² and its derivative. dy dx 4x(x – 3)(x – 6) to find each of the following. Find…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: The first derivative of the function h is given by h'(x) = tan(0.1x- x) for -n < x < R. On what…

A: Solution Given h'(x)=tan(0.1x3-x) for -π&lt;x&lt;π.we need to find on what intervals is h…

Q: 2. (a) Give the definition of the derivative f'(x) of the function f(x) in terms of a limit. (b) Use…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 00).…

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Q: 2.Given f(x)=5Vx-1, find f'(x)using the limit definition of the derivative.

A: Given f(x)=5x-1

Q: 4. The graph of the first derivative f'(x) of a functionf is shown below. At what values of x does f…

A: Given graph of f'(x) is The value of x where f'(x)=0 are called as critical values where extrema…

Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 -…

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Q: ose k is the derivative of K, a function with the same domain as k. inction K has one critical point…

A: According to answer policy we can answer one question at a time, therefore I will be answering first…

Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

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Q: The function f is continuous for all real numbers and the graph of its derivative function f' is…

A: Given The graph of the derivative of a continuous  f

Q: 3 5.) y = ; x+5

A: Given:- y = 3/(x+5) y = 3(x+5)-1 Using Formula : [f(x)g(x)]' = f(x)g(x)' + g(x)f(x)' Now, y' =…

Q: Find the value of a which makes the function below continuous on (-∞, ∞). f(t) = [a(x²/2) x < 1…

A: We will use the definition of continuity to solve this question.

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

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Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx&gt;1 Graph for this piecewise function is: B. Given function…

Q: Consider the function f(x)=ln (1+x2). a. Find all the critical values of f(x)=ln (1+x2). Using the…

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Q: 4x Consider the function f(x) : 3 – x a. Use the \underline{limit definition of derivative} to find…

A: We can solve all these points in the following way:-

Q: 5 Let f(x) =x -e*. Find the value of x for which the second derivative f“equals zero. 2

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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: 10.The graph of f'(x), the derivative of f, is given below for -6 Sxs7.On what intervals is the…

A: Option (c) is correct Because f'(x) is greater or equal to zero in that interval. Or we can say…