What is the slope of the tangent line to the graph of any quadratic function of the form y=ax²+bx+c at its vertex? a, b, and c are constants.

Q: Find all points of the graph of f(x) = 3x2 + 9x whose tangent lines are parallel to the line y - 57x…

A: Solution: Two lines are parallel if they have same slope.

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 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: 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 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: Find all points on the graph of ƒ(x) = 9x2 - 8x + 4 where the slope of the tangent line is 0.

A: ƒ(x) = 9x2 - 8x + 4

Q: Find all points (c, f(c)) on the graph of f(x) = x3 −3x2 where the tangent line has slope 9.

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Q: Find the points on the graph of f (x) = x3 − 3x2 + x + 4 where the tangent line has slope 10.

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Q: Find an equation of the line tangent to thegraph of ƒ(x) = x3 + 4x at (1, 5).

A: Given: The graph is expressed as fx=x3+4x To Find : Equation of line tangent to 1,5  The equation of…

Q: Find the point on the graph of y = 3x2 − 2x + 5 where the tangent line is perpendicular to the line…

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Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 15x + 10 with tangent lines parallel to the…

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Q: 5. Find the equation of the line tangent to the graph of f(x)= 2x' +4x² – 5x– 3 at | x = -1.

A: f(x)=2x3+4x2-5x-3diff w.r.t xf'(x) =6x2+8x-5now substitue x=-1f'(-1)=6(-1)2+8(-1)-5f'(-1)=-7slope of…

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: At what point on the graph of f ( x ) = 2x 3 - 3x 2 - 8x is the tangent line equal to 4?

A: Given that: fx=2x3-3x2-8x To calculate the slope of the tangent line of given function,…

Q: Find the equation of the tangent line to the graph of x4y16=1 at the point (81,1/3) and at the…

A: We use slope point form to equation of tangent line.

Q: Find the point (xo,yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent line…

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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: Find an equation of the line tangent to thegraph of f(x) =3/x at (2,3/2)

A: Given: y=fx=3x, 2,32 for finding of equation of tangent at given point we need slopem of tangent at…

Q: Find the point (xo, Yo) on the graph of y = x³ + 3x² + 5x – 3, at which the slope of the tangent…

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Q: Find an equation of the tangent line to the curve at thegiven point. y= 4x  - 3x2 ,    (2 ,-4)

A: we have to find an equation of the tangent line to the curve y=4x-3x2 at the point (2-4). as we know…

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: Determine the equation of the tangent line of the given function: f(x) = 3x² – 2x; (-1,5) y = -8x-3…

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Q: Find the equation of the line tangent to 3x²y + 4xy2 = 6x² + 5y at the point (1,).

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Q: At what point on the curve y = 2x²– 3x – 1 is its tangent parallel to the line y = 5x + 2?

A: Given curve is : y=2x2-3x-1 And the given line is : y=5x+2 We need to find the point on the curve at…

Q: The slope of the tangent line to the graph of the function y = 8Vx – 3 at (9, 21) is %3D 1.33 -2.33…

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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: Given :          y= x2-8x+9

Q: Find the equation of the line tangent to the graph of f(x) = 7x³ + 8x² – 2x – 6 at x

A: We need to find the equation of the tangent to the function f(x) = 7x3+8x2-2x-6 at x=—2 We know that…

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 slope of the tangent line to the graph at the given point. (x² + y²)² = 4x²y, (1, 1)

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Q: Find the slope of the tangent line to the graph at the given point. (x² + y²)² = 4x²y, (1,1)

A: To find slope of tangent of a curve at a given point, we need to find differential at that point

Q: Find the equation of the tangent to (x2+/ 5x2-Уг at the point (1,1). 8.

A: Given curve is: (x2 + y2)2 = 5x2 – y2and the given point is (x1, y1) = (1, 1)Equation of tangent…

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

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Q: Write the equation of the tangent line to the graph ofy = (7x2 − 6x + 2)(1 + 2x)atx = 1.

A: we have to find tangent line to f(x) at x=1first we will compute tangent point at x=1

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 equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

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Q: Find the equation of the line tangent to f(x) = 4x³ – 5x +4 at (–2, –18). -

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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 points on the graph of x5/2 + y5/2= 1 where the slope of the tangent line is -1.

A: Topic:- application of derivatives

Q: Determine the co-ordinates of all the points at which the tangent to the curve y = 3x'e8x is…

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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: What is the slope of the tangent line that touches the graph of In(y) + eA-=3y-4x at the point 3. 5

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Q: At what points on the graph of ƒ(x) = x3 + 6x2 + 21x + 2 is the slope of the tangent line 9?

A: Given:  f(x)=x3+6x2+21x+2Slope of tangent line=9 To Find: Points where the slope of tangent line is…

Q: Find the equation of the tangent line to the graph of y = x3 + 3x2 + 2 at its point of inflection

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Q: find the slope of the tangent line to the graph at the given point. (x2 + y2)2 = 4x2y,   (1,1)

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Q: At what point on the graph of y = (x^2)/2 is the tangent line parallel to the line 2x - 4y = 3? O…

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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 the function whose tangent line has the slope 8x² + 3 for each value of x, and whose graph…

A: To find the function: