Graph ƒ(x) = 1/(1 - x) and its quadratic approximation at x = 0. Then zoom in on the two graphs at the point (0, 1). Comment on what you see.

Q: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

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Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

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Q: Find the equation of the line tangent to the graph of y = 2x - 8x2 + 2x -6 at x = 2. | %3D

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Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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Q: Find an equation of the tangent line to the graph at the given point. x^2y^2-9x^2-4y^2=0, 4,2sqrt3

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Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

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Q: Hello. Can you please explain this problem to me?

A: Slope of the function is the derivative of the function.

Q: Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7)

A: We will find out the required equation of tangent.

Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

Q: Find the formula for a parabola with its vertex at (9,4) and with a second derivative of -3. f(x)=

A: let's equation of parabola is given by y=ax2+bx+c                                              ..1…

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope -12 at x = -1, and…

A: To find a parabola with equation.

Q: Find all points (x, y) on the graph of ƒ(x) = 3x2 - 4x with tangent lines parallel to the line y =…

A: Since the tangent is parallel to y = 8x + 5. Hence, the slope of the tangent = slope of the line = 8

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

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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: 4) Find an equation of the line tangent to the graph of 2x³y³ = 2y – 4x at the point (-1, –1). Show…

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Q: Find the shortest distance from x²+3y²=12 to the point (4,2).

A: We have to find the shortest distance from x²+3y²=12 to the point (4,2).…

Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: 2. Find the equations of both the tangent lines to the parabola y through the point (3, 16). :-

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Q: Find the point on the curve y = /2x + 3 which is closest to the point (5, 0).

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Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

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Q: 2. Find the equation of the horizontal asympto

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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: The slope of the tangent line to the parabola y = 2x“ + 2x + 6 at the point (1, 10) is: The equation…

A: Given,            The parabola is y=2x2+2x+6 and the point is 1,10.

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

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Q: The slope of the tangent line to the parabola y 4x + 7x + 5 at the point (0, 5) is: The equation of…

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Q: Find the equation of the line tangent to the graph of f(x) = 4x° + 6x2 – 6x – 5 at x = -6. %3D

A: The function is given by fx = 4x3+6x2-6x-5 To evaluate: The equation of the tangent line to the…

Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

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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: 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: 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: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: Find the point on the parabola y= -X-+4 whose tangent line is parallel with y= 3x-5,

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Q: Find the length of the curve (Sketch and Solve) One branched of the curve 9y2=4x3 from x = 0 to…

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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: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

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Q: Sketch the curve y = x/(x² – 9). Enumerate the steps in your solution.

A: as per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: Find the equation of the tangent and the nirmal to the curve y=5x4 at the point (1,5)

A: Given curve,  y = 5x4  To find the equation of tangent and normal at the point (1, 5)

Q: The slope of the tangent line to the parabola y 3x? + 2x + 3 at the point (– 5, 68) is: The equation…

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Q: Find all points on the curve 3x + 6y² = 36 where the tangent line also passes through the point (10,…

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Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

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

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Q: 4. Jacobi is seated on the line tangent to the graph of  y =2x3 -3x2 -12x +21 at x =2.

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Q: Find an equation of the tangent line to the graph of y = x³ - 3x - 1 at the point (2, 1).

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Q: Find the points on the graph of f(x) = 36x – 3x³ where the tangent line is horizontal. %3D

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Q: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: the equation of the tangent line to the graph of f(x) = 4x3 + 7x² - 8x – 6 at x = -1.

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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: Find the shortest distance from the origin to x2 − y2 = 1.

A: Definition used-         The shortest distance from a point to curve is the perpendicular distance…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.