Identify a function f that has the given characteristics. Then sketch the function. f(1) = 8 f '(x) = 4, -∞ < x < 0 f(x) %3D

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x;…

A: Determine the derivative for f(x). fx=lnx5f'x=ddxlnx5=ddx5lnx5×ddxx5=1x5×5x4=5xSo, f'x=5x

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: Differentiate  f and find the domain of f f(x)  =    ln ln ln x

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Q: 8. Consider the function f(x) = (x² + 1)e. (a) Show that the second derivative is f"(1) = (x – 3)(x…

A: Given function is

Q: Let f be the function defined for x > 0, with f (e) = 2 and f', the first derivative of f , given by…

A: (a) part Consider the given derivative of the function f'x=x2 lnx First, find the slope of the…

Q: Find the absolute extrema of the function on the closed interval.                   h(x) = x − 3√x,…

A: The given function on the closed interval [0,9] is

Q: Approximate the function at the value of x to four decimal places.

A: f(2)=ln 2+1+e2=ln (3)+e2

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = sin…

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

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Q: Find the absolute extrema of the function on the closed interval.                          y = tan…

A: Given function is y=tanx8.

Q: 5. Consider the function h(x) whose derivative h' (x) = 3x2Vx3 + 8. (a) Find functions f and g such…

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Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: Which of the following are local extrema (local maxima and local minima) of the function f(x)?

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Q: For a function f, we define the ___________________________________, denoted f’, by…

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Q: Show that the function f(x) = 1/2 e−|x|IR(x) is a valid pdf.

A: Let the function is given by, fx=12e-x      for Rx Further we simlified it as, fx=12ex      for…

Q: Find the intervals in which the function f(x)=sin (log,x)+cos(log,x)is decreasing.

A: By the first derivative test, a function is decreasing if its derivative is less than zero.

Q: A decreasing derivative f'(x) corresponds to a concave down function f. On which interval(s) is f…

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Q: Find any relative extrema of the function. f(x) = arctan(x) – arctan(x – 4)

A: Consider the given function  fx=tan-1x-tan-1x-4

Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

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Q: nd an example of a function f(x) such that the third derivative f"(x) is equal to 0 for all x, and…

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Q: The graph of a function f is given. YA Estimate 10 [20 1 0 1 f(x) dx using five subintervals with…

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Q: [-1,1] O (-1,1) O [-1,1) O (-1,1] O

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Q: Find the range and domain of the functions (1) f (x, y) = sin-(y-x)

A: We'll answer the first question. Since the exact one hasn't specified. Please re-submit the question…

Q: findthe domain of the function. f(x)=\sin e^{-x}

A: The domain of a function is the values of the variable that can be input into the function. The…

Q: Let f(x) = sin x, g(x) = cos x, and h(x) = 2x. Find the exact value of the expression, the average…

A: Given function: fx=sinx

Q: V2x Let F be the function defined by F(x) = || sin(4t + 1) dt. Find an expression for F'(x).

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Q: The function f is defined by f(x) = x² + 2 cos (3x + 3x). What is the average rate of change of f'…

A: Average rate of change of a function f on [a,b] is given by f(b)-f(a)b-a. Computing f(10) and f(3).…

Q: 3. Consider the function f(x) = e¯*. 4x2 – 2 (a) Show that the second derivative is f"(x) (b) Find…

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Q: Suppose that the only information we have about a function f is that f(1) = 5 and the graph of its…

A: Given graph, And also given f(1)=5. (a) The objective is to estimate f0.9 and f1.1 by using linear…

Q: Determine whether the function 1s differentiable. at, X=1$ then sketch a graph of ysf (x).

A: Step:-1 Given that fx = xif x≠12if x=1 And Right , left derivatives are respectively,   f+' 1…

Q: Write the composite function in the form f(g(x)) .[Identify the inner function  u =g(x) and the…

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Q: Consider the function f(x) = 3cos(2x). (a) Find the derivative of f(x). (b) Verify that the…

A: (a) Given function is f(x)=3cos(2x) The derivative, f'(x)=-6sin(2x)

Q: Q8. Identify the function, whose derivative is defined below: (x + h)2 – x? dy - lim dx h→0 h A.…

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Q: x20 is continuous at x-0, then a = a+sinx If the function f(x): 2+2acosx x<0 a. 1 b. -1 O c. 2 d. -2

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Q: Q21\ Find the value of (B) that make the function below continuous at x=0, tan 5x f(x) = x=0

A: NOTE: Refresh your page if you can't see any equations. . the function is continuous at x=0, when

Q: (b) Let f be a function such f(1) =2 and whose derivative is known to be f'(x) V+1. (i) Use a linear…

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Q: Consider the function f (x) = -2x ln x a. Find f' (x) b. Find the equation of the line tangent to…

A: Note: According to our expert guidelines only first three subparts are to be answered.kindly repost…

Q: Find any relative extrema of the function f(x) = arcsec x − x

A: Maxima: sec-1x -x=f(x) f'(x)=1xx2-1-1f''(x)&lt;0So f(x) has maxima value .

Q: consider a continuous function y = f(x) whose first derivative is y = x(x – 2). The graph of f has…

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Q: Q1) Find the derivative a) f(x) = arctan (e-2x) b) f(x) = [arcsin (2²)]³ C) f(x) = tan (lnx) + 52²

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Q: A) Consider the function f(x) whose second derivative is f’’(x)=4x+3sin(x). If f(0)=4 and f’(0)=4,…

A: According to the guidelines in case of multiple questions, We are only allowed to do first question.…

Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A: Integrate and pass that through given point for value of constant

Q: 1. What is dx [the function is f(x) = 1]?

A: To evaluate:

Q: 3. Consider the function f(x) = rl – 5x3. 10x + 10 (a) Show that the second derivative is f"(x) (b)…

A: Consider the given function, fx=x53-5x23 (a) Find the derivative of the function,…

Q: Draw a graph to match the description given. F(x) has a positve derivative over (- 0,-4) and (0,8)…

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Q: Find any relative extrema of the function f(x) = arctan x − arctan(x − 4)

A: Maxima or minima (relative extrema): Let f(x) is any function. 1) Evaluate f'(x)=0 for critical…

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: A function f(x) passes through the points (15,24). (18,37). and (22 Use this to approximate the…

A: Given, a function f(x) passes through the points (15, 24), (18, 37), and (22, 25).

Q: Can you help step by step please?

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Q: Find the derivative y' = f'(x) of the given function y = f(x). %3D Graph y = f(x) and y' = f'(x)…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…