If fx) =vx+2, and g(x) =f(x), find the slope of the curve g(x) = f -1 (x) at the point (2, 2).

Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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Q: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

Q: Find an equation of the tangent line to the curve y=2x^2+3 that is parallel to the line 8x-y+3=0

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

A: Given :y=x4+2x3-2x2-3x+3Line : x-3y=2

Q: Find the slope of the line tangent to the graph of x^2+2xy^2+3y=31 at the point(2,-3)

A: The slope of the tangent line can be calculated by using the derivative of the function at the point…

Q: At what point on the curve x = 3t2 + 5, y = t3 - 5 does the tangent line have slope ? (х, у) %3

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Q: find the slope of the line tangent to the curve x2=y2+3/2xy at (4,2)

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Q: At what point on the curve x 3t2 + 1, y = t3 - 5 does the tangent line have slope ? (х, у) -

A: We have given curve as x=3t2+1         ⋯⋯1y=t3-5           ⋯⋯2 From the equation (1) and (2), on…

Q: Find the slope-intercept equation of the tangent line to f (x) = 3x² – 4x + 5 at the point (1, 4).

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Q: The slope of a tangent to the curve f(x) = x² + 2x – 5 at the point (3, 10) is : 12 8. -5 10

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Q: Find an equation of the curve that passes through the point (0, 2) and whose slope is xy?

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Q: Find an equation of the tangent line to the curve y= x3 – 3x2 + 5x that has the least slope.

A: Given    slope is 1st derivative

Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

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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: 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 equation of the curve that passes through the point (1, 3) and has a slope of y/x2 at any…

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Q: Find an equation for the line perpendicular to the tangent line to the curve y = x3 - 4x + 1 at the…

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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: At what point on the curve x = 3t2 + 2, y = t3 – 2 does the tangent line have slope ? (х, у)

A: Slope of the line = dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now divide dy/dt by dx/dt.5

Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: find the slope of the tangent line to the curve X2-4X3y2=-2 at the point (1,1)

A: The given curve is,

Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

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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 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: Find an equation of the tangent line to the curve at thegiven point. y= 4x  - 3x2 ,    (2 ,-4)

A: we have to find an equation of the tangent line to the curve y=4x-3x2 at the point (2-4). as we know…

Q: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

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Q: Find the equation of the tangent line to the curve x2 + 4y2 = 8 and parallel to the line x+2y=8.

A: Given curve is x2+4y2=8. To find equation of tangent line to the given curve which is parallel to…

Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is parallel to the…

A: Given: y = 2x3-3x2-12x+20 Tangent line is parallel to x - axis. To find: The points on the given…

Q: write the equation of the tangent and normal line line of the curve. huow soution your 2. (3.0) f…

A: First, check if the given point lies on the curve, f(x) . If the point is on the curve, then compute…

Q: 9. Find the equation of the line tangent to the curve y = 3x5 + 10x³ + 15x + 1 at its point of…

A: the given curve , y=3x5+10x3+15x+1 we have to find the equation of the tangent line to the given…

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² - 2x³ at the point where x = a

A: given,y=3+4x2-2x3

Q: Find an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² − 2x³ at the point where x = a -

A: The equation of the curve is given by y = 3+4x2-2x3 To evaluate: The slope of the tangent to the…

Q: Find an equation of the curve that passes through the point (0, 6) and whOse slope at (X, y) is X/y.

A: Given that: Slope of the curve at (x, y)=xy

Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

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Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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Q: Find an equation of the tangent line to the graph of y = 2x² + 3 that is parallel to the line 8x - y…

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Q: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: Find the gradient of the curve . Y=4x^2 at x=3

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Q: What is the slope of the line tangent to the curve y = x4 – 8x3 + 22x2 – 24x + 9 at x = 1?

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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: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

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Q: Find the slope of the tangent line to the curve y 3x-8x + 7 at the point (-1,2). -3 3. -4 4

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

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Q: At what point (x,y) is the tangent line to the curve y=2x2-5x+8 parallel to the line y=3x-7

A: It is given that

Q: Find the equation of the family of curves whose slope at any point (x,y) is   2. x/y

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Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

Q: 2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3).

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Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

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Q: write the equation of the tangent and normal line line of the curve. huow somtion your 1 . f(x) = -…

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