Find the points of tangency of horizontal and vertical tangents to the curve r2+4ry+ 16y = 16.

Q: Find the points on the curve where the tangent is horizontal or vertical. x = - 3t, y = t² - 8…

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Q: Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d₂ pass through (-1, -1) and have at…

A: To Determine: Value of a, b, c and d so that curve y = a x3 + b x2 + cx + d

Q: On the curve y = x², find a point at which the tangent is parallel to the chord joining (0, 0) and…

A: To find the point

Q: The equation of the tangent line to the curve z +y = 25, at (4,-16) is 4 y%= %3D 16 16 (z - 4) + 16…

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Q: Find a point in the second quadrant on the curve 3x2 + 4y? + 4xy = 24 where the tangent line is…

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Q: Show that there is a line that is simultaneously tangent to both the curves y = ex and y = lnx.

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Q: Find the ABSOLUTE VALUE of the gradients of the tangents drawn to the ellipse x^2/4+y^2/93D2 at the…

A: We have to find absolute value of gradient at x=2 for the given function.

Q: Find the slope of the tangent line to the curve 2x + 2xy + 2y = 32 %3D at the point (-4, 2).

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Q: Find the points on the curve y = x3 + 3x2 - 9x + 8 where the tangent is horizontal. smaller x-value…

A: Explanation of the answer is as follows

Q: Find the length of the curve y2 = x3 from the origin to the point where the tangent makes an angle…

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Q: Find the slope of the tangent to the curve x^2+3xy+y^2=5 at (1,1).

A: The equation of the curve is given by x2+3xy+y2 = 5                           .......1 The point is…

Q: Find the slope of the tangent line to the curve (a lemniscate) 2 (z? + y?)° = 25(x² – y²) at the…

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Q: The slope 'mi of the tangent to the curvez= 3(5t+1)*andy=10+2 at t=2is,

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Q: Find the tangent and normal to the curve y=2e-x/3 at the point where the curve meets the y-axis

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Q: find equation for the lines that are tangent andnormal to the curve at the given point. ex + y2 = 2,…

A: Given: Equation of curve ex+y2=2 and the point 0,1, To find: Equation of tangent and normal line to…

Q: On the same axes, plot the curve y = 1x, the line y = x/8, and the tangent line to y = 1x that is…

A: Given curve is y=x. Let x,y be any point on the curve. Differentiate function with respect to x.…

Q: Find the points on the lemniscate where the tangent is horizontal. 8(x2 + y2)2 = 81(x2 − y2)

A: The equation for the lemniscate

Q: Find the points on the curve y = 2x' + 3x² – 12x + 1 where the tangent is horizontal. -

A: As per the instruction, we will be answering the first question. For (51), Given: y=2x3+3x2-12x+1.…

Q: Find the equation of the line tangent to the curve 3t2 + 8,y = 8t + 3 at t = 2

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Q: Plot the curve x³ + y3 = 6xy together with the tangent to the curve at the point

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Q: .find the points on the curve where the tangent is vertical x(t)=t^3-3t+2,y(t)=t^3-3t^2+2

A: Given: xt=t3-3t+2yt=t3-3t2+2 We first need the derivatives of parametric equations:…

Q: Find the points on the curve y = 2r3 – 3x2 – 12x + 20 - where the tangent is parallel to the x-axis.

A: A straight line parallel to x-axis have slope 0.

Q: 2) Find the points on the curve where the tangent is horizontal or vertical. x = t2 – 8t, y = 2t3 +…

A: A parametric equation of a curve is given by: x = t2 - 8t    and    y = 2t3 + 3t2  We have to find…

Q: Find the points on the curve where there is a horizontal tangent line: x = 5cos(t); y = t³ – 3t2 +…

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Q: Find the slope of the tangents to the curve at the points (P1 and P2) where it crosses (the x-axis.…

A: The curve will cross the x-axis when it's y intercept become zero.   Slope of curve at any point is…

Q: Find the equation of the tangent line to the curve 2y? + xy = 5 – 2x², at the point (1;1).

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Q: find the acute angle between the curves y=x^3-6x^2-11x-35 and y=x^4-4x^3-27x^2-40x at their points…

A: Given: y=x3-6x2-11x-35y=x4-4x3-27x2-40x To Find: The acute angle between the curves at their points…

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 3 where the tangent line is horizontal. (x, v) =…

A: Solve the following

Q: Find the equation of the line tangent to the curve x = 3t2 + 8 , y = 8t + 3 at t = 2

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Q: Find the point (in the first quadrant) on the lemniscate 2(x2 + y²)² = 25(x² - y²) where the tangent…

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Q: Find the point on the curve y = xe* where the %3D tangent is horizontal

A: Slope of tangent to the curve y=f(x) is defined as mT=dydx(x, y). Slope of horizontal tangent is…

Q: Find an equation for the horizontal tangent to the curve at Q. y = 1+ v2cscx + cotx

A: To find tangent line , find out the slope of the tangent line Take derivative to find out the slope…

Q: Determine the point(s) where the tangent to the curve is horizontal: y = (x2 + 2x + 1)(x2 + 2x + 1)

A: Given problem:- Determine the point(s) where the tangent to the curve is horizontal:   y = (x2 + 2x…

Q: Find the slope of the tangent line to the curve I defined b y 5x²+8xy-4y"= 1B47 atthe point %3D…

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Q: Find the slope of the tangent line to the curve 3z? – 2xy – 3y3 = 63 at the point (3, – 2).

A: topic - slope of tangent line to curve

Q: Find the acute angle between two tangent lines at point of intersection between two curves xy = 5…

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Q: find the points on the curve where the tangent is horizantal, X=t^2+1,y=3t^2+t

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Q: On the curve y=x2 ,find a point at which the tangent is parallel to the chord joining (0,0) and…

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Q: Find the point on the curve y=/2 for which the tangent ine to the curve is perpendicular to the line…

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Q: Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal. a)…

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Q: IL Find the acute angle between two tangent lines at point of intersection between two curves xy =…

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Q: Find an equation of the tangent to the curve r + ry + y² = 3 at (-2, 1). %3|

A: First find the slope of the tangent with the help of derivative of the curve than write the equation…

Q: On the curve y=x2,find a point at which the tangent is parallel to the chord joining (0,0) and (1,1)

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Q: . Determine the points where the curve 6x+ 4y-y=6 has a vertical tangent line. p. Does the curve…

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Q: What is the slope of the line tangent to the curve y = 3x² + 6x +3 at x = 4? Oy' = 51 O y' = 30 O y'…

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Q: Find the slope of the tangent line to the curve 2x + lay 4y 20 at the point (2,- 2).

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Q: Find an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find an equation of the line tangent to the curve y = v4x – 3 – 1 and perpendicular to the line x +…

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Q: Find the points on the curve y = x3 + 3x2 9x + 4 where the tangent is horizontal. smaller x-value…

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Q: The equation of the tangent line to the curve z? + y² = 49, at (9,-15) is , %3D 15 - (z – 9) + 15 15…

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