If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

Q: Find all points (x, y) on the graph of g(x) = x3/3 -3x2/2+1 tangent lines parallel to the line 8x -…

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Q: Find the equation of the tangent line to y = 2"-5a -5x+1 = 4. at x = y = 12 In 2 - 1

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Q: Find the equation of the tangent line to the curvey = √2-4 at the point (5, 1). Oy=2-1 Oy= 22-2 Ov=z…

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Q: Find the equation of the tangent and normal line of the function f(x) = V2x – 1 at the point (5, 3).

A: fx = 2x-1     , 5,3f'x = ddx2x-1     = ddx2x-112        = 122x-1ddx2x-1        = 222x-1 = 12x-1∴f'5…

Q: An equation of the tangent line to the curve y= 4x2-8x-5 at the point (-1, 5) is O y14x-9 Oy 14x71 O…

A: The curve is given by,

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 the slope of the line tangent to the curve x - 3xy + 4x = 2 at x = 1. -5/3 O 2/3 O 1/3 O 4/3

A: The given curve is: x3-3xy+4x=2 We need to find the slope of the line tangent to the given curve.…

Q: Find the equations of all tangent lines to the curve x² + 4y2 = 8 that pass through the %3D point…

A: The curve x2+4y2=8 that pass through the point (-4, 0). We have to find the equation of all tangent…

Q: Find all points (x, y) on the graph of ƒ(x) = 3x2 - 4x with tangent lines parallel to the line y =…

A: Since the tangent is parallel to y = 8x + 5. Hence, the slope of the tangent = slope of the line = 8

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

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Q: The tangent line equation of 2x6+y4=9xy at the point (1, 2) is ... ....E Persamaan garis singung…

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Q: Find the point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

Q: Find equations for two lines through the origin that are tang net to the curve x²-4x+y²+3=0 .

A: We have given equation of curve x2-4x+y2+3=0. We also know that the slope of the line will be the…

Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: The equation of the line is      x+2y-6=0⇒y=-12x+3       in the form of line equation y=mx+c  So,…

Q: ) Find the equation of the tangent line ETL for f(x) = x³ - 2x +1 at x = −1

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Q: Find the equation of the tangent line to the curve y = x+5x* which is passing through point (1, 3):*…

A: Given : Curve  y = x + 5x2 Point 1,3   To find : The equation of the tangent line to the given…

Q: Find the equation of the tangent line to f(x)=xe2x-2 + 3 at the point (1,4).

A: Slope of a tangent of a function at a point is equal to the value of the derivative at that point.To…

Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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Q: Find the line tangent to the curve x + yi = 4 at the point (3V3, –1). y = x- 4 Oy = x+4 y = O y= s…

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Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

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Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: Find the point (xo,yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent line…

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Q: Find the point (xo, Yo) on the graph of y = x³ + 3x² + 5x – 3, at which the slope of the tangent…

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Q: Find the tangent and normal line to the curve at the specified condition. 12x2 - 20y2 = 55 parallel…

A: Given that the curve is 12x2-20y2=55 and the required tangent and normal line is parallel to the…

Q: Find an equation of the tangent line to the curve y = 2x2 +3 that is parallel to the line 82 – y + 3…

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Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Find equations of the tangent lines to the curve х — 1 x + 1 that are parallel to the line x – 2y =…

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Q: 9. Find the equation of the tangent line at point (2,2) on the curve fx) = x²- 7x + 12.

A: To find the equation of the tangent line

Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

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Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: What is the value of the first order derivative of the closed function given as…

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Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: Find the point (x0, yo) on the graph of y = x + 9x² + 8x – 5, at which the slope of the tangent line…

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Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: 24)) Since the tangent of the curve y = x ^ 5 + ax - 3 at the point x = 1 is y = x -b, then b =?

A: Given that y=x-b is the tangent of the curve y=x5+ax-3 at the point x=1.

Q: Find the critical points of y= -2x^2 +4x +3 and apply the Second Derivative Test to find the maximum…

A: Critical point and extreme points

Q: Find the equation of the tangent line to 4x2 +y2= 8 at (1,2)

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Q: Find all points on the curve y = x³ + 2x² - 6x + 5 where the tangent is parallel to the line 2x + y…

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Q: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

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Q: Find all points on the curve 3x + 6y² = 36 where the tangent line also passes through the point (10,…

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Q: Find the x-coordinate of the point/s on the curve y = 2x – 3x² – 12x + 20 where the tangent line is…

A: The slope of the tangent line to the curve at point P(x,y) is given by,…

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: Find the point on the parabola y= X- + 4 whose tangent line is parallel with y = 3x -5

A: Let a point on the parabola is h,k. Now the slope of the tangent line is given by: m=dydxh,k Since,…

Q: Find all points (x, y) on the graph of f(x) = x° - 5x + 26x + 19 with tangent lines parallel to the…

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Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

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Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: