Unbelievable shapes can be created by using the implicit plotting capabilities of a computer algebra systems. Use a graphing calculator or graphing system to graph the curve: y(v -1)(v–2)=x(x-1)(x-2). Include an image or sketch of the resulting graph. 1. At how may points does this curve have horizontal tangent lines? Estimate the x-coordinates of these points. 2. Find the equations of the tangent lines at the points (0,1) and (0,2) 3. Find the exact x-coordinates of the point where the curve has horizontal tangent lines. 4. Create even more fanciful and unbelievable curves by modifying the equation. Include the modified equation and a sketch or image of the graph.

Q: 1 ) Find the equation of the curve for which   y” =  6x – 4 and which passes through (1,2) and (-2…

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Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = (1/3)x - (1/2)x² -…

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Q: Suppose a curve is defined by the equation 16(x² + y²) = 45. Show that if you translate the curve to…

A: we have to translate the curve.

Q: How will you sketch the graph of y =x (x-1)4 with respect to the x-axis? O A. sketch it tangent at…

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Q: The curve's equation is given by x* + y4 = x² + y?

A: Here is the solution of the given problem.

Q: II DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y= (1/3)x - (1/2)x² - 2x…

A: 2) y=x2+22 discuss the properties of the curve vertical asymptotes since there is no value of x for…

Q: The curve-4x - 3y3-7x + 5y = 2 is shown in the graph below in blue. Use the graph below to draw line…

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Q: Consider the curve y = 4x3. The sketch of the portion of this curve between x = - 1 and x = 8 is…

A: Solution..

Q: Locate the points of inflection of the curve y = (x^2)(e^x) * -2± /3

A: Solve the following

Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

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Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y= (1/3)x - (1/2)x² -…

A: As per bartleby guidelines we only give first question answers.

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 7. Y= 3x-5x³ + 4 8. Y (2x-…

A: Given function is y=3x5-5x3+4 Given function is polynomial function Domain: The set of all real…

Q: 4 Find a. the equations of the tangents to the circle x'+y +4x-2y-24 0 at the points where the…

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Q: 5) The circle defined by the equation x + y = 18 has two points where the slope of its tangent line…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: 4 Find a. the equations of the tangents to the circle x + y +4x - 2y - 24 = 0 at the points where…

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Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 7. Y=x³ – 3x? 8. Y= (2x–…

A: 7.)  y = x3 - 3x2 Properties of the curve:   The function takes zero at x= 0 , 3     It has local…

Q: Given the equation of curves: y = x2 + 7x + 6 and x - 2y = 6. Find the slopes of the tangents of the…

A: We begin by finding the points(s) of intersection of the 2 curves y =x2+7x+6  &  x-2y = 6y…

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx b) y = -

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Q: A curve is defined by the equation xy - 6+x?y = 0. (a) Verify that the curve passes through the…

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Q: The graph of x +y = 25 is a circle having center at the origin and radius 5. a. Write the equation…

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Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 2. y = (x2 – 3)2

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Q: No calculators. Find the exact length of the curve. y=2+2x³/2, 0≤x≤1

A: Given curve is, y=2 + 2x32,  0≤x≤1 Find the exact length of the curve. Length of the curve:…

Q: 4. An arch is to be constructed so that its shape follows the curve y=-x +10x, where x measures the…

A: GIven equation of the curve is, y=-12x2+10x where x be the horizontal distance along the ground. y…

Q: The curve -4x – 3y³ – 7x + 5y = 2 is shown in the graph below in blue. Use the graph below to draw…

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Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has a x-…

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Q: The line y = ax + b is tangent to the graph of y = x3 at the point P = (-3, -27). Find a and b.

A: The line y = ax + b is tangent to the graph of y=x3 at the point P=-3,-27. we have to find the…

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x – 3x? + 4x – 12…

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Q: (y – 3)2 = 4(x - 5), (6, 5) %3D y = Parabola 6 (6, 5) 6 10 12 14 -2

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Q: 13. y = x², y = 0, x= 1; about the y-axis

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Q: 1. Trace the curve whose equation is x* – x' y = -7x² + x+6 х* + 3х-10 Identify the following a.…

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Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y= (1/3)x – (1/2)x² -…

A: A real-valued function shows various properties such as symmetricity, passing through the origin,…

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

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Q: Given the equation of a family of a curve, find the general solution from the choices below. x3 y² =…

A: Given that: y2=x3c-x     NOTE: As per our answering guidelines, we can only answer 1 question or 3…

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x³ - 3x? + 4x- 12…

A: y = x3 - 3x2 + 4x - 12y = x2(x -3) + 4(x - 3)y = (x2+4)(x - 3)   X-intercept: (3, 0)    [Real values…

Q: Two curves with equations y = 6e¬* + 1 and y = 8 – e* are shown in the graphs below.

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Q: Find the exact length of the curve. y2 = 16(x + 5)3,   0 ≤ x ≤ 1,  y > 0

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Q: The curve defined implicitly by the equation 2x2 + xy + 5y? = 30 is shown below. y 4 2 -2 2 -2 -4 dy…

A: Since you have asked multi-part question, we will solve first three sub part. For other part please…

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric equation of curve is x=t3+1,    y=t3-1,     -2≤t≤2. This implies that, x=t3+1,…

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x3 – 3x? + 4x – 12

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: 3 y Vsec4t – 1 dt, 0, 4 4 Find the length of the defined curve. (write your solutions in detail and…

A: To find the length of the defined curve: y=∫0xsec4t−1dt,  −π4≤x≤π4

Q: Any help will be useful.

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Q: Discuss the properties of the curve and sketch fully: a) y = x2 e-x b) y = 1+lnx

A: To sketch the curve : a) y = x2e-xb) y = 1 + ln xx

Q: If b, c, and d are constants, for what value of b will the curve y = x3 + bx2 + cx + d have a point…

A: Given y = x3 + bx2 + cx + d  b, c, and d are constants

Q: Discuss the properties of the curve (w/ solution) and sketch fully: y = x?e-*

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Q: Find the exact length of the curve. 23/2 12, 0 <x < 1 y =

A: Given : y=23x32,       0⩽x⩽1   To find : Curve length

Q: 4 Find a. the equations of the tangents to the circle x +y +4x-2y – 24 = 0 at the points where the…

A: Given,  (a) Equation of the circle   x2+y2+4x-2y-24 = 0  We have to find the equations of tangents…

Q: A graphing calculator is recommended. (a) If G(x) = 5x2 - x3, find G'(a) and use it to find…

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Q: d the exact length of the curve. =√y (y - 3), (y - 3), 4 ≤ y ≤ 16

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Q: If you will draw the graph of y=x^2 (x-1), how will the graph behave at the x-axis?   A) The graph…

A: y= x2(x-1)at x = 0:y = 0(0-1)y = 0and at x=1, y=12 (1-1)Hence, The graph crosses (0, 0) and (1, 0).

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.