Fanciful shapes can be created by using the implicit plottingcapabilities of computer algebra systems.(a) Graph the curve with equation y(y2 - 1)(y -2) = x(x - 1) (x - 2)At how many points does this curve have horizontaltangents? Estimate the -coordinates of these points.(b) Find equations of the tangent lines at the points (0, 1)and (0, 2).(c) Find the exact -coordinates of the points in part (a).(d) Create even more fanciful curves by modifying theequation in part (a).

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 81x2…

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Q: X = --6t-1 2 Find all points on the graph of that have either a vertical or horizontal y=- -9t +1 3…

A: Here given x=3t22-6t-1y=t33-9t+1

Q: Find an equation of the tangent line to the graph at the given point. (y - 3)2 = 4(x- 5), (9, 7) %3D…

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Q: The slope of the tangent line to the parabola y = 2a2 + 2a + 6 at the point ( – 2, 10) is: The…

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Q: 1. Find the equation of the family of curves and the equation of the particular curve that passes…

A: Given the slope of the tangent at any point (x,y) is  1)3x+4 2)(x+2)/(1-y) We need to find the…

Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

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Q: the equation of the tangent line to the parabola at the given point.

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Q: Find an equation of the tangent line to the graph of y=-8x/x^2+1 at the origin and at the point…

A: To find the slope of the tangent we find dy/dx We will use the quotient rule

Q: Find the equation of the line tangent to the curve. y= -3x + x^2 +2 at the point (3,2) Include y= in…

A: The given equation of the curve: y=-3x+x2+2

Q: The slope of the curve defined by the equation y-x + x =-2 at the point (-1,0) is %D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: The equation of the tangent line to the curve y at the point (2, 5. written in point-slope form is:

A: find equation of tangent line

Q: Find an equation of the tangent line to the graph of the equation at the given point. y = 9-x2; P…

A: Solve for the equation of the tangent line

Q: Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the…

A: We have to find an equation of the tangent line to the curve at the given point.…

Q: Find an equation of the curve that passes through the point (3, 1), and has the given slope y′ = −…

A: Given that y'=-y5xdydx=-y5x

Q: A curve passes through the point (0,5) and has the property that the slope of the curve at every…

A: Slope of the curve is given by dy/dxdy/dx is twice the y coordinate. So, dy/dx=2y

Q: Therefore, the curve y = x* - 2x2 + 2 has horizontal tangents at x-0, 1, and -1

A: Just compute the derivative and equate it to zero.

Q: What are the coordinates of the points in the graph of y2-x²+ 6x – 13=0 in which the tangent line is…

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Q: 13) Find the equation in slope-intercept form that is tangent to (x- 1)² + (y + 2)² = 25 and passes…

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Q: Draw a diagram to show that there are two tangent lines to the parabola y = x² that pass through the…

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Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: A curve passes through the point (0, 5) and has the property that the slope of the curve at every…

A: A curve passes through the point (0, 5) and has the property that the slope of the curve at every…

Q: The tangent line to the curve y = x3 - 6x2 - 34x - 9 has slope 2 at two points on the curve. Find…

A: Given,  The tangent line to the curve y=x3-6x2-34x-9 has Slope=2 at two points on the curve.…

Q: The slope of the tangent line to the parabola y 2x2 + 2x + 4 at the point (0, 4) = The equation of…

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Q: 8. A curve whose slope at any point is 6x² А. у %3D 2х3 — х? +х+6 - 2x + 1 passes through the point…

A: We need to find equation of curve.

Q: ve passes through the point (0, 9) and has the property that the slope of the curve at every point P…

A: Topic:- application of integration

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 slope of the tangent line to the parabola y = x2 at the point (2, 4) by analyzing the…

A: We have to find the slope of tangent line to the given parabola y=x2 at the point 2, 4 by analyzing…

Q: Find the point (x0,y0) on the graph y=x^3 + 6x^2 +3x -5 at which the slope of the tangent line has…

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Q: Q3/ Line A with equation y = -8x - 18 is tangent to the curve with the equation y = 4x + 2x². Find…

A: Tangent line: If a line touches a curve at a unique point then the line is called tangent and that…

Q: Draw a diagram to show that there are two tangent lines to the parabola of  y = x2  that pass…

A: Given the parabola : y=x2Tangent passes through the point 0,-9 We need to find the coordinates of…

Q: The slope of the tangent line to the parabola y = 3x + 3 + 4 at the point (5, 94) is: 33 The…

A: Equation of parabola y=3x2+3x+4 The slope of the parabola at any point is calculated as  dydx=6x+3…

Q: Find the equation of the tangent line to the curve at the given point. Illustrate by graphing the…

A:

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: Find an equation of the tangent line to the curve at the given point. y = 4x^2 − x^3, (1, 3)…

A: The curve y = 4x2 – x3, we have to find the equation of the tangent line to the curve at the point…

Q: 6. Find an equation in the form y = ax³ + bx² + cx + d__whose graph has an x-intercept at x = -1, a…

A: Given: x-intercept at  y = 2 y-intercept at x = -1 slope at (-2,-2) is 5. (-2,-2) lies on the curve…

Q: The slope of the tangent line at any point (x, y) on the curve 3x2 - 2x+7 and the point (1, 3) is on…

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Q: or the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

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Q: 2-x )Use the guidelines of this section to sketch the curve y3x-12VX.

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Find an equation of the curve that passes through the point (1, −2), and has the given slope y′ =…

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Q: Find the equations of the tangent lines to the graph of y=x²+6 that go through the point (0,-2) and…

A: Given problem:- Find the equations of the tangent lines to the graph of y = x2 +6 through the point…

Q: Does the parabola y = 2x2 - 7x - 1 have a tangent whose slope is -1? If so, find the point of…

A: Recall: Slope , m= dydx Point - slope intercept form : (y-y1)=m(x-x1) ; where 'm' is the slope

Q: The slope of the tangent line at any point (x, y) on a curve is 2vx. If the point (9.3) is on the…

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Q: Find the equations of the tangent lines to the circle x2 + y2 = 9 which pass through the point (-7,…

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Q: Find an equation of the curve that passes through the point (8, 2), and has the given slope y′ =…

A: Solution:-We have to find an equation of the curve that passes through  the point (8,2) and having…

Q: The slope of the tangent line to the parabola y 3x + 3x +7 at the point (- 5, 67) is: The equation…

A: Take the derivative and put the given point.

Q: The graphs of ƒ(x) = x² + 5 and g(x) = -x² + 2 share two common tangent lines. Find the equations of…

A: Here we will find the equation of common tangent,

Q: Find an equation of the tangent line to the curve at the given point. y = 7x2 - x3, (1, 6) y =…

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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), (9, -1)…

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Q: Find the equations of the tangent lines to the circle x2 + y2 = 1 which pass through the point (-4,…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.