Find the maximum, minimum or inflection point of each of the following curves. (For numbers 1-5) [5]y=4x/(x²+4)

Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation.

Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: Find the equation for the curve in the xy-plane that passes through the point (1, -1) if its slope…

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Q: Find the points on the graph of y = x2 + 3x − 7 at which the slope of the tangent line is equal to…

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Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: Find the equation of the line tangent to the graph of y = (x3 - 1)(x2 + 1)4 at the point where x =…

A: The Slope of the line at any point is given by the derivative of the function at that particular…

Q: Find the points at which the graph of this equations has vertical or horizontal tangent lines:…

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Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

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Q: Locate the points of inflection of the curve y = (x^2)(e^x) * -2± /3

A: Solve the following

Q: Find the points on the graph of y = 1– 5x + 3x² where that tangent line is parallel to the line y –…

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Q: Find an equation of the line tangent to the given curve at a. y = x3 – 4x2 + 2x – 1; a = 2

A: Slope m of the tangent will be given by dydx Therefore, dydx=ddxx3-4x2+2x-1 ⇒dydx=3x2-8x+x…

Q: what would the equation of the tangent line to the graph of y=(4x^4-3x-1)/(3-x^2) be at x=1

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Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 7 at the point (3, 2.1). y =

A: Given curve is Differentiating with respect to x, we get

Q: Find an equation of the line tangent to the curve defined by x2 + 6xy + y 32 at the point (2, 2).…

A: v

Q: Determine the equation of the line tangent to the graph of y = x° + 2x at the point (1, 3).

A: y=x3+2x   x1,y1 =1,3dydx=3x2+2slope of tangent at point1,3dydx1,3=312+2 = 5Slope of the tangent m =…

Q: Find the coordinates of the points on the curve y = x³ - 6x² + 14x – 12 at which the tangents have a…

A: We will differentiate with respect to x and equate the same to 5 and find the points.

Q: Find the point on the graph of y = 3x2 − 2x + 5 where the tangent line is perpendicular to the line…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6,5) ||…

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Q: Find the length of the curve with equation x2 (y + 1)3 from the point where æ = 0 to the point where…

A: Since the given curve is  x2=y+13      from point x=0 to x=33. Given curve can be written as x=y+132…

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line.…

A: Given equation of a graph is 4x2+y2-8x+4y+4=0 Since we need to find the points where the tangent to…

Q: Find the equation of the family of curves whose slope at any point (x,y) is 3x2+4

A: To find: the equation of the family of curves whose slope at any point (x,y) is 3x2+4  We know that…

Q: 4)Solve for the family of curves of straight lines with y-intercepts thrice as their corresponding…

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Q: Find the length of the following curve. y = 3x 2) fromx = 0 to x= 8

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Q: After Identifying and sketching the curve for x2+25y2-4x+100y + 4 = 0, partimize the curve

A: Given: x2+25y2-4x+100y+4=0 To Find: i. Identify and sketch the curve.ii. Parametrize the curve.

Q: Find the equation of the langents to the graph y-x3 3x2-15x-20 at the points of the graph where the…

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Q: 4. Find the equation for the line tangent to a. y= x²- 3 x + 5 at the point (2, 3)

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Q: Find an equation of the curve that passes through the point (0, 2), and has the given slope y′ =…

A: y'=x4y, (0,2) Formula ∫xndx=xn+1n+1+C

Q: Find the member of the curve whose slope at any point is 2e** and passes through the point (0, 1)

A: We need to find the member of the curve whose slope at any point is 2e^(4x) and passes through…

Q: Find the eqaution of the curve that passes through (0,1) if its slope is given by y'=1/2X at any…

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Q: Find the slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

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Q: Find a point on the graph of the curve y = (x - 3), where the tangent is parallel to the chord…

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Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: 9. Find the points on the graph y = 7x - where the slope of the tangent line is parallel to x-2 28x…

A: To find- Find the points on the graph y = 7xx - 2 where the slope of the tangent line is parallel to…

Q: The curve is given by 2 + 1), 0<x<3. 3

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Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: Find the length of the curve defined by y = 4x3/2 + 11 from x = 2 to x = 8.

A: We will differentiate the function and use the arc length formula.

Q: Find the points where the graph of 2y-x+4x-6y+1=0 has horizontal or vertical tangents.

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Q: Find the equation of the curve whose slope at any point is In and which xy2 passes through the point…

A: Point (x1 , y1) = (1, -2) Slope = ln1xyxy2

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A: Solution of given question is written in below steps.

Q: find the slope of the curve at the point indicated y = x - 1/x + 1, x = 0

A: Given, y=x-1x+1 and the point x = 0

Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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Q: Find the length of the curve : y = + from x = 1 to x = 3 - 3 4x

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Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: Use the methods of this section to sketch the curvey =  x3  -3a2x +2a3, where is a positive…

A: The curve is  y =  x3  -3a2x +2a3, where is a positive constant.

Q: Find the exact length of the curve. X=1/3sqrt(y)(y-3), 9 less than or equal to Y less than or equal…

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Q: Find the equation of a family of curves which are -2 defined by f'(x) = (x + 1)3

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Q: 1 Find the length of the curve ソ= 9 from x =1 to x=2. 28x7,

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