Determine the nature of the turning points for the curve y = x5 – 5x* + 5x³3 – 1.

Q: Use the guidelines of this section to sketch the curve   y =  x - 3x 1/3

A: Let us make a table for the function x -8 -1 0 1 8 y -2 2 0 -2 2

Q: Determine the values of x where a curve y = x3 - 3x2 - 9x+ 12 has horizontal angent lines.

A: Given,         y=x3-3x2-9x+12

Q: Use the guidelines of this section to sketch the curve. x2 - 25 y = x2 - 5x

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Q: Find the point of inflection of the curve y = x^3 - 6x^2 - x + 12. (-2,6) (2,-6) (-2,-6) (2,6)

A: We have to find point of inflection of given function.

Q: Find the point of inflection of the curve 6x – x' +5 y = 7 b. (2, 4) d. (3, 1) а. (0, 1) с. (2, 3)

A: Inflation point of a curve is a point on the curve at which concavity of the curve changes means it…

Q: For the curve y = x² - 2lnx, locate all critical points and points of inflection.

A:

Q: Find the points of intersection of the line y = 5 x with the curve y = 3 x + x^2

A: In order to find the point of intersection of given line line and curve , we must find values where…

Q: Use the guidelines of this section to sketch the curve.   y = 2√ x    -x

A: We will make a table for the function  x 0 1 4 9 y 0 1 0 -3

Q: Find the exact length of the curve = √(y - 3), 1 ≤ y ≤

A:

Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

Q: Use the guidelines of this section to sketch the curve   y =x / ( x3  -1 )

A: Given: To sketch the given curve using the guidelines.

Q: Use the guidelines of this section to sketch the curve  y =   x4  -4x

A: We have given the curve; y =   x4  -4x

Q: Evaluate the length of the curve x = 5 - y+1,0<y<3

A: Given, x=5-y+1 ,     0≤y≤3

Q: Identify and sketch the curve for x2-y2-6x = 0

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Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

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Q: Determine the coefficients a, b, c, d that will make the curve y = ax3 + bx2 + cx +d passes through…

A: Given y=ax3+bx2+cx+d

Q: Use the guidelines of this section to sketch the curve.   y = x/ x2-9

A:

Q: Use the guidelines of this section to sketch the curve.   y =  x4 - 4x

A:

Q: Find the exact length of the curve. y = 5 + 2x³/2, 0< x < 1

A: Given: y=fx=5+2x32, 0≤x≤1 we know that lengthL of curve in interval a,b is given by L=∫ab1+f'x2dx…

Q: Use the guidelines of this section to sketch the curve   y = x (x- 4 )3

A: Consider the given function: y=xx-43 Now make a table for function value at different points:

Q: What is the equation of a family of curves orthogonal to 2x2 + y2 = c?

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Q: Find the exact length of the curve. 2. y = 3 x3/2 Osxs1

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Q: Find a possible point of inflection of the curve y x +3x2 + 6x

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Q: Find the length of the curve X= -y², 1≤ y ≤9

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Q: Find the coordinate of the local maximum for the curve 21 y=2+9x- +2x

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Q: Use the guidelines of this section to sketch the curve.   y = 2 + 3x2 - x3

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Q: Determine the length of the curve x = 3y2 -1 between y = 0 and y = 4 3/2

A: The given curve is x=3y32-1 We will find the arc length of the curve between y=0 and y=4

Q: Use the guidelines of this section to sketch the curve.   y= 3√(x2  -1)

A: We need to find the x intercept, y intercept, vertical asymptotes, horizontal asymptote etc to…

Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: Use the guidelines of this section to sketch the curve.   y = x √(5- x)

A: We can not have negative number inside square root So, 5-x≥0 x≤5  Let us make a table of values x…

Q: Find the point of inflection of the curve x^3 – 3x^2 –x + 7.

A: For inflection point, second derivative is zero

Q: Find the length of the curve y = x3/2 from x = 0 to x = 3.

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Q: Find the point of inflection of the curve y = x^3 - 6x^2 - x+ 12. O (-2-6) O (2.6) O (2. -6) O…

A:

Q: Use the guidelines of this section to sketch the curve.   y = x 5   - 5x

A: We make a table with different values of x and y.  x y  0 0 1 -4 -1 4

Q: Use the guidelines of this section to sketch the curve.   y = x2/ x2+ 9

A:

Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

Q: Sketch the curves 1.) y = 3+4x-x2

A: the equation of the curve is: y=3+4x-x2 we have to sketch the given curve.

Q: Find the exact length of the curve. y = 5 + 8x/2, 0<x<1

A: Topic = application of derivatives

Q: Find the following points of intersection.

A: Given that, y=42xy=2x2

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: Find the slope of the curve y² = 3x + 1 at the point (- ,0). Draw the graph of the curve.

A: y2=3x+1 Differentiating with respect to x, we get 2y·dydx=31+0⇒2y·dydx=3⇒dydx=32y Now slope of the…

Q: Identify and sketch the curve for: x2-y2-6x=0

A: Combine the like terms of x and y in the given equation, and then add 9 on both sides of the…

Q: nsider the curve x3 + y2 - 4xy = -2

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Q: Evaluate the length of the curve y = 3 + 3Vx +1 , 0<x< 3

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Q: Locate the inflection points of the curve y = e²x²

A: The given curve is y=e2x2. The first derivative of y=e2x2 is, y'=ddxe2x2=2xe2 The second derivative…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.