sketch the approximate shapes of the graph of the two functions on the same axes without using a calculator. Explain how the graphs of f(x) and g(x) are different from each other and how could you obtain the graph of g(x) from the graph of f(x). Find the points of intersection of the curves, if any. f(x)=arctan x g(x)=f(x)+3

Q: Find the point on the graph of f (x) = (9x + 8)/æ + 5x (x > 0) at which the tangent line is…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given point.…

A: Given,f(x)= -2x +5 and the point (1-,7)

Q: The derivative in question, solve f´(2) if f(x) = x^3 – 6x^2 + 9x + 3 Determine the largest and…

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Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: Given the function g(x) = 2^x , along with the tangent line to the graph at x = 0, may you help me…

A: g(x)=2x  , Tangent line at x=0 Apply definition of derivative g'(x)=limh->0.01g(x+h)-g(x)hReplace…

Q: Determine analytically the point (s) at which the graph of the function has a horizontal tangent. x2…

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Q: Find the domain of the function. f(x) = ln ( 1/ (x + 1)

A: f(x)=ln1x+1

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = a - 3x + 2

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = (1 −…

A: The equation of the function  f(x) = (1 − x)(x2 − 3)2

Q: Find the equation of the tangent line to the graph of the given function at the given value of x.…

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Q: Given the function g(x) = 8x³ + 12x² – 48x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 19 – x²;…

A: The given data is: gx=19-x2 To find the slope of the tangent line at the point 3,10.

Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

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Q: Sketch the graph of the function y=ln(x+1)−1.

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Q: Let P=(x,y) be a point on the graph of y=x2-5  a) Express the distance d from P to the origin as a…

A: P=(x,y) be a point on the graph of y=x2-5

Q: sketch the graphof the function and state its domain. f (x) = 4 ln(x − 2) + 1

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: The tangent line to the graph of f(x)= 5-x+e^(x-1) is horizontal at what  point?

A: Calculus Question

Q: The function g is difirentiable and satisfies g(-1)=4 and g'(-1)=2. what is the approximation of…

A: given g(-1)=4 and g'(-1)=2.         g(-1.2)=?

Q: Given the function g(x) = 8x* + 84x² + 288x, find the first derivative, g'(x). = (x),6 Notice that…

A: Since, you have ask multiple part's in the question. I am answering for first three parts. Please…

Q: Find the inflection points of the function f(x) = ln(x^2 + 1)

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Q: Fill in each blank so that the resulting statement is true.

A: The slope of the tangent at a point on the curve is equal to the value of the derivative of the…

Q: Find the equation of the line tangent to the graph of the given function at the point with the…

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Q: 4) Find the values of x where the tangent lines to the graph of the function is horizontal. f(x) =…

A: a) Consider the function fx=xx2+16. To identify the x values where the tangent lines to the graph of…

Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: Find f′​(x) and find the equation of the line tangent to the graph of f at the indicated value of…

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Q: Find an equation of the tangent line to the graph of the following function f at the specified…

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Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: Find the equation of the line tangent to the graph of the given function at the point with the…

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Q: For what value(s) of x does the graph of f(x)=10x^3 − 90x^2 + 240x +90 have a horizontal tangent?…

A: To find the slope of the tangent we find f'(x)

Q: 1. Sketch the graph of the function 4x f(x) = x E (-00, 00) 1+4x² Be sure to calculate the local…

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Q: Find the inflection points of the function f(x) = x 2 ln x

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Q: 4)Find the inflection points of the function . f(x)=ln(x^(2)+1)

A: In this question we will find the point of inflection   we have given function   f(x)=ln(x2+1)…

Q: If f (x)= x2 - 4x, at which point on the graph f (x) is the tangent line horizontal

A: topic - slope of tangent line

Q: Determine an equation for the line tangent to the graph of the given function at the indicated point…

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Q: Find the first and second derivatives of the following functions and use them to sketch a graph. f…

A: Please refer to the image below

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: Find the equation of the line tangent to the graph of f at the indicated value of x.   f(x)=8−7…

A: Givenf(x)=8-7lnx

Q: Given the function g(x) = 8x° + 12x2 – 480x, find the first derivative, g' (x). g'(x) = Notice that…

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Q: The graph f(x) has horizontal tangents when x = 3 f'(x) 2+ 2 -1 0

A: Horizontal tangents have slope = 0. ie slope of tangent = f'(x)

Q: If f(x) =2x2 - x3 , find f'(x) , f" (x), f"'(x) , and  f(4) x.Graph f , f' , f" , and f"' on a…

A: Given: f(x)=2x2-x3Differentiating f with respect to x  ⇒…

Q: Find all the values of x where the graph of f(x) = 2x³-36x2 + 192x 9 has a horizontal tangent line.…

A: topic - derivative of a function and point of horizontal tangent line

Q: 6. Find the values of x for which the line tangent to the graph of f (x) = 4x2 – 3x + 2 has a…

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Q: Find the equation of the function f whose graph passes through the point ( 0, and whose derivative…

A: We have to find value of f(x)

Q: Find the equation of the line tangent to the graph of f(x)= -(1/6)x^2 at x=3

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Q: What is the derivative of f(x) = -3? Do not include "f'(æ) =" in your answer. For example, if you…

A: Given            f(x)=-3

Q: Use the graph of the derivative g'(x) shown below and the terminology: increasing, decreasing, local…

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Q: Find a function with the given derivative whose graph passes through point P f'(x)=x-4, p(1,7)

A: Integrating on both sides, we get

Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: Topic = Derivative