(a) Use the definition of derivative to determine whether the parabola y = 2x2 – 13x + 5, have a tangent whose slope is –1. If the tangent exists, find an equation for the line and the point of tangency. If not, why not?

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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Q: (a) Find all the points on the graph of (x² + y? + y)2 x² + y? that have horizontal tangent line.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the equation of the line tangent to the graph of y = (x3 - 1)(x2 + 1)4 at the point where x =…

A: The Slope of the line at any point is given by the derivative of the function at that particular…

Q: 4) Find the equation, in slope-intercept form, of the tangent line to the graph of : y = Vx2 + 11 at…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Show that the x-coordinate of the vertex of the parabola whose equation is y = ax2 + bx + c occurs…

A: Given the equation of a parabola y=ax2+bx+c

Q: Find the points at which the graph of this equations has vertical or horizontal tangent lines:…

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Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: The slope of the tangent line to the parabola y= 4x2 + 2x + 4 at the point (-1, 6) is : ?  the…

A: Consider the equation of the parabola, y=4x2+2x+4 The first derivative dydx of the curve at any…

Q: A coordinate of the point on the curve of y=2x3−3x−6, where the tangent at the point is…

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Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

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Q: リ= 3x3-x2+6

A: Given query is to find the equation of the tangent.

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 coordinates of the points on the curve y = x³ - 6x² + 14x – 12 at which the tangents have a…

A: We will differentiate with respect to x and equate the same to 5 and find the points.

Q: Find a parabola with equation y = ax² + bx + c that has slope 4 at x = 1, slope -16 at x = -1, and…

A: We know slope of a curve y=f(x) is given by, dydx=f'(x)

Q: a) Use the definition of derivative to determine whether the parabola y = 2x² – 13x + 5, have a…

A: Derivative y with respect to x and then equate it to the given slope to find x coordinate of the…

Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6,5) ||…

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

A: Given equation of a graph is 4x2+y2-8x+4y+4=0 Since we need to find the points where the tangent to…

Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: Find an equation of the tangent line to the parabola y − x2 - 8x + 9 at the point (3, -6).

A: The derivative of a curve at a point gives the slope of the tangent to the curve. It can be…

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: (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an equation of the tangent line to the…

A: Given:f(x)=5x(1+x2) Formula: ddxf(x)g(x)=g (x)f'(x)-f(x)g'(x)g(x)2

Q: Find the equations of the tangent lines to the parabola y = -x² + 5x – 6 at its points of…

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Q: Find the slope of a line tangent to the curve of the given equation at the given point. y = x2 - 3;…

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Q: Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).

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Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

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Q: The x-coordinate of the point where the tangent line to the parabola y=2x^2 at x=1 intersects the…

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Q: if f(x)=6x^2 - 4x, find f'(2) and use it to find the equation of the tangent line to the parabola…

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Q: What is the slope of the tangent line to the graph of any quadratic function of the form y=ax²+bx+c…

A: First find the vertex of the parabola, y=ax2+bx+c . Then, compute the expression for dydx .…

Q: Find an equation of the tangent line to the parabola y=x2  -8x+9 at the point (3, -6)

A: Given :          y= x2-8x+9

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: 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: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

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Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

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Q: a) Find the points at which the tangent line to the graph of function f(x)=2x²-24x+6 has slope equal…

A: Let y=f(x) be any function, then    Slpoe at any point, m = df(x)dx

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A: Solution of given question is written in below steps.

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

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Q: Find the equations of the tangent lines to the parabola -x² + 5x – 6 at its points of intersection…

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Q: Find the equation of the tangent line to the graph of the given equation at the specified point. y =…

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Q: Determine the equation of the tangent to the graph of y = x³ - 3x² + x+ 3 at the point x = -1

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Q: Find the equation of the line tangent to the parabola y = x^2 -1 at the point (-2,3).

A: Given the parabola :

Q: Find all the points of the graph of y = (x - 2)2 at which the tangent line is perpendicular to the…

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Q: At the two points where the curve x2 - xy + y2 = 36 crosses the x-axis, the tangents to the curve…

A: x2-xy+y2=36

Q: At what point does the graph of the function f(x) = x³ – 3x has horizontal tangent ? Find equations…

A: a) Points are (1,-2) and (-1,2) b) Lines are y=-x-1, and y=-x+3

Q: The slope of the tangent line to the parabola y=2x^2+2x+7 at the point where x=4 is: slope =…

A: The equation of the parabola is y=2x2+2x+7

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: At what point of the parabola y=x -3x+5 is the tangent line parallel to the line 3x-y 2?

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Q: Find an equation of the tangent line to the graph at the given point. x²y? - 9x? - 4y² = 0, (-4,…

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Q: At what point on the parabola y=3x^2+2x is the tangent line parallel to the line y=10x-2? Use first…

A: We have to find the point.

Q: (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an equation of the tangent line to the…

A: Consider the given function as y=5x1+x2