q.no Use a graphing utility to graph the two functions f (x) = x2 + 1 and g(x) = lxl + 1 in the same viewing window. Use the zoom and trace features to analyze the graphs near the point (0, 1).   Which function is differentiable at this point?

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)…

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Q: 4. The graph of the first derivative of a function ƒ is given below. yA y= f'(x) 3 5 7 (a) On what…

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Q: find the points of inflection and discuss theconcavity of the graph of the function. y=x-\ln x

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Q: F(X)

A: y = f(x) is continuous at x = a  only if following properties are satisfy : (1)  f(a) exists . (2)…

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Q: Given the function g(x) = 8x – 84x? + 240x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: Where is the function f(x) =| x | differentiable?

A: Given information: fx=x The function, after removing modulus function, y=x=x,      x>0=-x,…

Q: Describe how you could use the graph of f(x) = 2" to obtain a decimal approximation for V2.

A: y=2x

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Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent. (x, y) = Need…

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Q: Suppose that flx) is a differentiable function and g(x)=(x+2)/f(x). If f(0)= 22 and f(0)=5, then…

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Q: Determine all points at which h(x) is differentiable. Justify your answer. 9 – x2

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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: 10. Find a function y = ax +bx+c whose graph has an x-intercept of 1, a y-intercept of -2, and a…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Which of the following is the x-coordinate of a relative extremum of the function f(x) = = Arct…

A: We will use first derivative test to determine the extremum of the function.

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: 2 For what values of x does the graph of f(x) = 2x° + 3x – 180x – 1 have a horizontal tangent line?

A: First we find the derivative of f(x), the slope of f(x) for horizontal tangent is 0 and the…

Q: The graph of f', the derivative of the function f, is shown below for the interval 0<xs10. The areas…

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Q: A major car company analyzes its revenue, Ríz), and costs Cx), in millions of dollars over a…

A: The revenue function and the cost function is given as:…

Q: Find the values of a and b so that f will be differentiable at x = 3.

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

A: Given f(x)=sinx4         , 0, 8π

Q: Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find…

A: The given function is f(x)=3x^2+2.

Q: Consider teu tunction: fcx) = -x+2x +4 Calculate f(x +h) for any constant h f(x +h) - f(x)

A: The given function is fx=-x3+2x+4. (a) Evaluate f(x + h) as  follows.…

Q: Describe the domain of the function f(x, y) = ln(4 x - Y).

A: as per guideline i am answering one question .please give a like !

Q: The derivative of f is xʻ(x-2Xx+3). At how many points will the graph of ƒ have a relative maximum?…

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

A: Follow the procedure given below.

Q: O For what value of x does the function f (x) = 4x2 – x +1 have a horizontal tangent?

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Q: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x? – 12x + 5 b) Determine…

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Q: Let f(x) = 33 –x The slope of the tangent line to the graph of f (=) at the point (-5, 8) is The…

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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: 3. a) Use the Chain Rule and the fact that |x| = Vx2 to show that d dx |x| b) Sketch the graphs of…

A: We will use the give solution as we are instructed.

Q: -he deriva tive of the function y= tan'( 3x+1) when X-0: %3D

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

A: Given- fx=sinx4,0,8...........(1) As we know that inflection point is a point on the graph at which…

Q: Consider the function f(x)=(x+1)(x–1)2, At what value of x will the graph of f cross the y-axis?…

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Q: What is the equation for a linear function with a vertical stretch/compression by 2/5. BE SURE TO…

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Q: 6- For the function y=lnx a- Describe what type of function it is. b- How is the function related to…

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Q: Let f(x) = 9 – x² The slope of the tangent line to the graph of f(x) at the point (-3,0) is The…

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Q: 3. Consider the function 8x f(x) = + 15. - The tangent line to the graph of f at the point (6, f(6))…

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Q: There is a bacteria cell in a Petri dish that is reproducing at a rate of              r(t) = 2t^2+1…

A: Solution:

Q: 8. Given the function f(x)%=2x3 -5x3 , find the point where the tangent is horizontal to the curve.

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Q: 4. a) Find the value of x where the function f(x) = (x – 4)3 is not differentiable.

A: According to power rule of differentiation , .

Q: 1. For the function f(x) = 3x? + 8x – 2, (a) Find the slope of f(x) at x = 3 | (b) Find equation of…

A: According to the bartleby guidelines, for more than one questions asked, only the 1st question…

Q: 11. Use the definition of the derivative to find f'(x) for the function f(x) = x2 + x + 2. Show your…

A: We have to find the derivative of the given function.

Q: 2- Calculate the extremum point of below function and Classify it f(x) = 4 x3 + 2 v11 – x + x?

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Q: 6. Determine the inflection points and intervals of concavity for the function y= e2*

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Q: Q9. For what values of x does the graph of f(x)=x-2sin(x) have a horizontal tangent? *

A: As per Bartlebys expert answering policy, we can only answer one question with its three subparts,…

Q: Let f(x)= 1/(3x+2) find the values below 1) f(x+h)= 2) (f(x+h)-f(x))= 3) lim h→0 (f(x+h)−f(x))/h 4)…

A: Let f(x)= 1 / (3x+2)Part 1)f(x+h) = 1 / [3(x + h) + 2] = 1 / (3x + 3h + 2)

Q: The slope of the tangent line to the graph of f(x) at the point (3, 7) is The equation of the…

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Q: 3. Use the graph of y = f (x) shown to sketch the graph of its derivative f'(x). [if on your own…

A: Give function f(x) has graph If you see this graph you will observe that derivative of f(x) will be…