Sketch the graphs of y= f(x) and y=- given that: f(x) f(x)=4x² –1 - a b f(x)=sin(x)+1 given 0

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -5 and g'(3) = 2.…

A: Here, y = g(x)  and g(3) = -5 i.e. when x1 = 3, then  y1 = -5 and g(3)=2 i.e. At x =3, the slope, m…

Q: Determine the missing coordinates of the points on the graph of the function

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Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

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Q: Find an equation of the line tangent to the graph of G(x) = 4 e - 7x at the point (0,4).

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Q: 12. Given the point ( 2, 1) on a tangent line to the curve ƒ(x) = x² − 2x + 5 find the point(s)…

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Q: Let g(x) = x 3. Calculate g'(a), and explain why g' does not exist when a = = 0. Sketch a graph of y…

A: Consider the function: gx=x23g'x=ddxx23Apply the Power Rule:   ddxxa=a⋅xa−1…

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule…

Q: Find an equation for the line tangent to the graph of 2x f(x) %3D x + 4 at the point (2,…

A: The standard form of the tangent helps to find the required equation. The standard form of the…

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -6 and g'(2) = 4.…

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

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Q: The graph of 3 (x+y) = 25 (x -y²), shown in the figure, is a lemniscate of Bernoulli. Find the…

A: Given query is to find equation ifbthe tangent at given point.

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

A: Given function is y=tanx8.

Q: Consider the graph of f (x) = 16 – x². f(x) P Find the coordinates of the point P in the graph at…

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Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

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

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Q: For what values of x in [0,2pi] does the graph of f(x)= x + 2sin(x) have a horizontal tangent?

A: Horizontal tangent:The slope of a tangent of the graph of a function f (x) is df (x) ∕dx. For a…

Q: Find the arc length of the graph of the function f(x) = 2√³ from * = 2 to x = 6.

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Q: 2. Find the equation of the secant line on the curve f(x) = -x² +2 passing through the points ro =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.

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Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x<03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

Q: Find an equation of the tangent line to the graph of the function f defined by the given equation at…

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Q: How is the graph of g(x)=2sin(3x) related to the graph of f(x)=sin x? GRaph the function g(x), show…

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Q: Sketch the graph of the following between x = 4T and x = = 47. y = sin x 0.5+ -Зл -27 2л Зл 47 -0.5+

A: We have to sketch the graph

Q: 5. Let f(x) = 5x4 -+ 8Vx - 3. x2 (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.______

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Q: Find the lengths of the curves y = sin -1x - √(1 - x2), 0≤ x ≤ 3/4

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Q: Find the lengths of the curves y = x2 - (ln x)/8, 1≤ x ≤ 2

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Q: 2) Find the point(s) at which the graph of f (x) = has a horizontal tangent. x2+1 %3D

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Q: 7) Find the tangent line to the graph of f (x) = 3 – 4e * at x =0.

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Q: The point (2,1) is on the graph of x2 . y3 + 5· x² = y² + 23. Find the slope of the line tangent to…

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Q: 6. Determine the x-value(s) of the point(s) on the graph of f (x) = 3x³ – 11x – 2 where the tangent…

A: The function f(x)=3x3-11x-2 where the tangent line is parallel to the line 10x-2y-18=0

Q: True or False The graph of y = cos x is decreasing on the interval (0, π).

A: True or False The graph of y = cos x is decreasing on the interval (0, π).

Q: Use the graphs to approximate the number of points of intersection of the graphs of y1 and y2 y1 = 3…

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Q: Does the graph of Sxsin(1/x), x + 0 g(x) 1o. x = 0 |have a tangent line at the origin? Give reasons…

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Q: х2—4 Use the guidelines for sketching the curve f (x) = ln х2-3х-4.

A: please see the next step for solution

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: The tangent plane to the graph of at the point where (x, y) = (2, 2) (write the appropriate function…

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Q: Sketch the graph of the following between x = 4T and x = 4т. y = sin x 0.5 -Зл -2л 2л 47 -0.5-

A: y=sinx between x=-4π and x=4π

Q: 69. Find a cubic function y graph has horizontal tangents at the points (-2, 6) and (2, 0). = ax +bx…

A: The form of cubic function is given as follows.

Q: 1- Find the equation of the tangent to the curve y = 2 sinx+ cos2x at the point x =a. 2- Find the…

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Q: 41. Find the points on the graph of f(x) = 5- 2 sin.x, 0<x 27, at which the tangent line is parallel…

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Q: On the graph of f(x)=sinx and the interval [0,2π), for what value of x does the graph cross the…

A: Plot the graph of sinx given below

Q: 9) Find the point(s), if any, where the graph has a horizontal tangent for 3x4 %3D = - 3x2 f(x) = 4…

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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: Sketch the graph of y = -3 sin(x) on the axes below. 4 3 2 -7/2 7/2 37/2 27 -1 -2 -3 -4

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Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

Q: 24. Consider the graph of y = Use limits and 1+ eax first derivatives to determine how the shape of…

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Q: 1- Find the equation of the tangent to the curve y= 2 sin x+ cos2x at the point x = n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Choose the correct graph of y = sin x, - T < x < 2 T; and y = csc x, - T < X< 2T: 2 1 27 -1 -2

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