The graph of y = f(x) is in the figure below. Does the function f(x) appear to be continuous on the given interval? f(x) (a) 0 < x < 2 f(x) v continuous on the given interval. (b) 0 < x< 0.5 f(x) continuous on the given interval.

Q: Find the value k that makes the function continuous. (ka?, x > -2 f (x) kx + 18, x < -2

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Q: Given the derivative f′(x), find the x-value for all relative extrema for the graph of the original…

A: Answer

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

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Q: Using the criterion of the first and second derivatives, find the graph of the function c) F(x) = x…

A: Topic = Functions

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Q: The graph of the continuous function g, the derivative of the function f, is shown above. The…

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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: 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: True or False The function f(x) = 2x/(x - 3) has y = 2 as a horizontal asymptote.

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Q: Given the graph of the derivative f'(x) shown below, which one of the following statements regarding…

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Q: 24: Find the extreme points of the function f(x) = x + y ху On the circle x+y=2

A: We shall find out extreme points of the function in the next using the a equation of circle.

Q: Use the graph of y = f(x) to sketch the graph of its derivative f(x). y 20 16 12 하 4 -5 -4 -3 -2 -1…

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Q: The graph of f(x) passes through the point (-1,4), The slope of the line tangent to the graph at the…

A: The slope of the tangent of the function at a point is given by the derivative of the function at…

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: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = f(x), evaluate…

A: Finding the g'(4) from the given conditions.

Q: Find the slope of the secant line between x = -1 and x = 2 on the graph of the function f(x) = -2x +…

A: The given function is fx=-2x3+3. Compute the slope of as follows.

Q: Find k such that the line is tangent to the graph of the function.

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Q: ecos-1 x if x 1

A: If a function has to be continuous  then it must to follow below Left hand limit = Right  hand limit…

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

A: Calculus Question

Q: Find k such that the line is tangent to the graph of the function  Function: f(x)=k square root x…

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Q: Find the absolute extrema of the function on the closed interval.                      g(x) = 6x2/(x…

A: Given    g(x)=6x2x-2 ;  -2,1

Q: The total number of local maximum and minimum points of the function whose derivative, for all x, is…

A: 1st derivative of function is f'(X) =x(x-3)^2(x+1)^4 For critical point we must have f'(X)=0 Hence…

Q: Given the derivative f'(x), find the x-value for all relative extrema for the graph of the original…

A: Consider the given derivative. f'x=x2−5x+6 Put the first derivative equal to zero.…

Q: Sketch the graph of f(x) = x lxl. Then show that f '(0) exists.

A: A function is a relation which maps each value in domain to exactly one value in range.  For a…

Q: Find the point on the graph of the function that is closest to the given point. f(x) = /x, (3, 0)…

A: Given, y = f(x) = x Let's assume the closest point to (3,0) will be (x, y) then (x,y) = (x, x)…

Q: Suppose that the differentiable function y = g(x) has an inverse and that the graph of g passes…

A: Given,

Q: Find the domain of the function: f(x) = ln(3 - x)

A: The Domain of a function Includes all values of x for which the function is defined. We know that a…

Q: . Sketch the graph of the unit step function, denoted by U and defined by U (x) = {0 1 if if x<0 0sx

A: Ux =0x&lt;01x≥0 So this step function is equal to 0 when time t is negative and is equal to 1 when…

Q: Let f(x) = 4x3 + + 2Vx – 7. Find f'(x). 15. Find an equation for the tangent line to the graph of…

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Q: 2. For what values of x does the graph of f(x) = x³ + 3x² + x + 3 have a horizontal tangent line.

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Q: 1 Find the distance between the two values of x at which the function is discontinuous. x²-3x + 2

A: The function given is ,f(x) = 1x2-3x+2f(x) is discontinous when,x2-3x+2 = 0Using quadratic formula,x…

Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

Q: The location of the point of inflection in the graph of the function y = x ln x is

A: Given: y = x ln x

Q: Use the Intermediate Value Theorem to show that the graph of f(x) = 4tan(x) – x + 1 intersects the…

A: Please note that according to guidelines only first Q is solved. Please repost the other question.

Q: The graph of  f(x)  and a line tangent to the curve at  x = 4  are shown. If  g(x) = sqrt(f(x))…

A: In the question it is asked to calculate the value of g'(4) for g(x)=f(x). for the graph given…

Q: Given the function g(x) = 6x³ + 27x² 72x, find the first derivative, g'(x). g'(x) = 0 when x = -4,…

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Q: True or False The graph of the function f(x) = x2 is increasing on the interval [0, ∞ ].

A: The statement: The graph of the function f(x) = x2 is increasing on the interval [0, ∞ ].

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = V f(x), evaluate…

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

Q: Find the function f(x) given that f ′ (x) = e x + x and the graph of f passes through the point (0,…

A: Given: f'x=ex+x &amp; Px,y=0,3   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Sketch the graph of the function  f(x) = ln∣x∣ and state its domain.

A: Sketch the graph as shown below:

Q: Find the absolute extrema of the function on the closed interval. f(x) = x3 - 12x, [0,6]

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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: The graph of the derivative f' of a continuous function f is shown. (Assume f' continues to o.) y y…

A: Given that: Graph of f'(x)

Q: The graph of f (x) = ax+b x²+3x-8 has horizontal tangent at (2, -1). Determine the values of a and…

A: Given query is to find the value of a and b.

Q: 3. Is the function given by g(x) = x² x = 4? Why or why not? 3x continuous at

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Q: Consider the following function. f(x) = x* + 4x3 + 11 (a) Make a sign diagram for the first…

A: We have to find the sign diagram for first derivative,  sign diagram for second derivative,  sketch…

Q: At the point x = 2, the function J x-2 -< rs2 -8 2<x< f(x) = is (a) continuous and differentiable…

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Q: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of g at x=3 is…

A: Given that: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of…

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

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Q: Find the intervals on which the function is continuous. y = 서+2 7 |

A: Please rate and feel free to ask any query about any part of the question.