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: What is the most time-consuming part in using a graphing utility to graph a general second-degree…

A: To discuss about graphing utility.

Q: For the implicitly defined equation, consider the following. 6 7. (-1) -3 -2 -1 1. 2 3 (a) Find the…

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Q: #2.) Calculate the slope of the tangent to the given function at the given point or value of x b.)…

A: 2.b) gx=x+2, P-1,1d) fx=5x-2, P4,52 Note:     multiple questions are given, we are answer only one…

Q: 4) Determine an equation for the tangent to the graph of the curve y = (6x - 3)(-x? + 2) when x = 1.…

A: Note: To draw the tangent of a curve at a given point, first we have to find out the slope of the…

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Given,  y=2-5x2

Q: Find the equation of the tangent line to the graph of the function ?(?) = −(? + 8)2 + 4 at the point…

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Q: Line has equation y = 17-4x and passes through point P which has coordinates (k-1, k + 1). (a) Find…

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Q: The equation y-(5)=2(x-(3)) in slope intercept form is y=?

A: The equation y-(5)=2(x-(3)) in slope intercept form is y=?

Q: The graph of f(x) = where these horizontal tangents occur? 2x+3x – 120x + 20 has two horizontal…

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Q: If f(x) = 2x? - 9x + 4, find the equation of the line tangent at a = 2.

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Q: Find the equation of a curve going through the point (3, 7) and having slope 4x² – 3 at (x, y).

A: Given ,Slope of curve is 4x2-3Thereforedydx=4x2-3Taking integationon both…

Q: Give an equation for the tangent line to = 1 at the y2+1 point (5,2) and sketch it on the graph. -5-…

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Q: The graphs of the equations (x - 3)2 + (y - 5)2 = 10 and x2 + (y + 1)2 = 25 intersect %3D at

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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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.