Provide an appropriate response. Find all points (x, y) on the graph of f(x) = 2x2 -3x with tangent lines parallel to the line y = 13x + 8. (4, 32) (4, 20) (0, 0), (4, 20) O (8, 20)

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A: Given , the function f(x) = x2 - 2x Now we find      f(1) = 12 - 2•1 = 1 - 2 = -1,…

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A: Given a Line L which is perpendicular to  y = (2/3)x  at point (3,2)  Equation of line L is…

Q: 4. For what values of x does y² – 2x3 – 12x? = 0 have horizontal tangent lines? A. x = 0 only В. x =…

A: The value of x for function Horizontal tangent lines ?

Q: Where does f(x)=x³-3x²+2x -7h have tangent lines that are parallel to y 2x-7? Selected Answers:

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Q: he slope of the line tangent to the curve y = x -8x3 + 22x2 - 24x +9 at x=1 is (a) -2 (b) 2 (c) 0…

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Q: Find an equation of the tangent line to the graph at the given point. 3(x² + y2}² = 100(x? – y²),…

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Q: Q2: Find the points on the curve y 2x3 -3x2 -12x + 20 where the tangent is a. perpendicular to the…

A: Curve y = 2x3-3x2-12x+20 To find the points on the curve y where tangent is   Perpendicular to the…

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: Find the point on the graph of y = x3 such that the tangent at the point is parallel to the line y –…

A: Consider a graph: y=x3……1   Equation of line parallel to the tangent of above equation is:…

Q: C. Find the slope and the equation of the tangent line to the 21 21 = 3x al 28. y=x²-3x+3 at (3, 3)…

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Q: Find y' and the slope of the tangent line to the graph of (3x - 5y)5 = 2y2-9 at the point (3,2).…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the given…

Q: Find the equation y = f(x) passing through the points (-11-21), (1,15), (2,12) and (3, 3)? Find also…

A: We will use the Lagrange interpolation method. We have: x x0=-1 x1=1 x2=2 x3=3 y y0=-21 y1=15…

Q: 2. (6 marks) Find the slope of the line tangent to f: y = 2/5x + 1 at the point (3,8). c) - D) E) -…

A: Answer and explanation is given below..

Q: Find y' and the slope of the tangent line to the graph of (2x - 5y)7 = 3y2 -2 at the point (3,1).…

A: The used formulas are

Q: 8. The line y = -4x + b is tangent to the curve f(x) = 2x² – 8x + 12. Determine the value of b. %3D

A: The equation of the tangent at a point h,k on a curve y=f(x) is given by, y-k=f'(h) (x-h)

Q: find an equation of the tangent line f(x)=x+(6/x)    points (x,y)= (-6,-7)

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Q: Find the point on the curve Y = √x closest to the point (3,3)

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Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

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Q: 2. Find the slope of the curve at the point indicated. a. y = 5x – 3x²,x = 1 x-1 b. y =,x = 0 x+1

A: Find the slope

Q: B. Find the slope of the curve at the given point. 1. y = 4 – 3x2 at (-1, 1) 2. y = x2 – 5 at (1,…

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Q: 5. Find the slope for f(x, y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: To find the slope for function f at point P in the direction of the line from M to N.

Q: Use calculus to find the point on the curve y = 3x−1 that is closest to the point (2, 0).

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Q: 3. If f(3) = 2 and f'(3) = -4 , find an equation of the tangent line when x = 3. %3D %3D А. у%3D2 (х…

A: Given : f(3)=2f'(3)=-4

Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: 5. Find the slope for f(x,y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

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Q: Find an equation of the tangent line to the graph at the given point. 3(x2 + y?)² = 100(x² – y²),…

A: Given that       the equation is 3(x2 + y2)2 = 100(x2 - y2) The point is (x1, y1) = (4, 2) We have…

Q: Find the x value of the point on the curve y = 3x + 2 closest to the point (1, 0).

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Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

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Q: Find the equation of the line tangent to the curve f(x)=x+ at the point (5, 26/25) 1 %3D

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Q: Which of the following is/are points on the curve y = x4- 8x3 + 22x2 - 24x + 9 where the tangent…

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Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: Find an equation of the tangent line to the graph at the given point. 3(x2 + y?)² = 100(x² – y²),…

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Q: 49. Find the slope of the curve y = (2x2 - x+ 3)(x + x+1) at (1, 12).

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Q: 10. Find the points of inflection of the curve y f(x)=x³ -x.

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

Q: 2а3x at (a, a) ,2 x2+a²

A: Given curve is,

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: Find y' and the slope of the tangent line to the graph of (2x - 5y)7 = 3y2-2 at the point (3,1).…

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y

A: Given problem is : Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn…

Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: B. find the slope of the tangent to the curve at the given point 1. y= x-6, (1, - 2) 2. y = 3x -5x.…

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Q: Where on the curve of 1 does the tangent have the greatest positive slope? y = 1+ x? O 1) 3 3 O 2) 3…

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