At what point does the graph of the function f(x) = x³ – 3x has horizontal tangent ? Find equations of all lines having slope -1 that are tangent to the curve y = I-1°

Q: Find an equation of the line tangent to y = xinx at the point x = 1.

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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 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: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

Q: Find the equation of the tangent line to the curve y²(y² – 4) = x² (x² – 5) at the point (0, –2). |

A: Equation of tangent line is given by:y-y1=dydxx=x1·(x-x1)      .............[1]So first find dydx at…

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 an equation for the line perpendicular to the tangent line to the curve y = x3 - 4x + 1 at the…

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Q: 3. Find the equation of the tangent line to the curve y = x2 - 3x + 4 that perpendicular to the line…

A: we have to find the equation of the tangent line to the curve y=x2-3x+4 that is perpendicular to the…

Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

Q: 5. Find the equation of the tangent lines to the curve y = x² + 3x -4 and parallel to the line 6x…

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Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: FInd the equations of the tangent lines to the curve y=(x-5)/(x+5) that are parallel to the line…

A: Given:The equation of the curve is y =(x-5)/(x+5).The equation of the line is x-10y =2.

Q: Find the equation of the line tangent to the graph defined by the equation at the point (2,0).…

A: Given equation of curve ,xey-y=2 -1

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 an equation of the tangent to the curve f(x) = 2x2 - 2x + 1 that has slope 2.

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Q: Find an equation for the line tangent to the graph of  f(x)= 2xex at the point (3,f(3)). y=?

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Q: Find an equation of the line tangent to the curve defined by æ° + 2xy + y% = 104 at the point (2,…

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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: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: Find an equation of the tangent line to the graph of y = 2x/x2+1 at the origin and at the point…

A: use differentiation for finding the slope and then use slope intercept form for finding the tangent…

Q: Find an equation of the line tangent to the curve y = x²e*-3 at x = 3.

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Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: Explanation: Given that,  y=2x3-3x2-10x+1     Concept Used: 1. Slope of the tangent is the first…

Q: Find an equation for the line tangent to given curve y = -10z2-3 4r+1 3 at x = 0-

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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 the equation of the tangent line to the curve x2 + 4y2 = 8 and parallel to the line x+2y=8.

A: Given curve is x2+4y2=8. To find equation of tangent line to the given curve which is parallel to…

Q: Determine the equation of the line tangent to the graph given by y = at the point x +1 (4, }).

A: To find the equation of the line tangent to the graph y=xx+1 at the point 4,25

Q: Find the equation of the line tangent to y = x2 - 1 going through x = 1

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Q: 4. Find the equation of the curve for which y""= 2x³. The slope of the inflectional tangent at (-1,…

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Q: Find the equation of the line tangent to the graph of f(x) = −2x² + x + 3 at x = 1. Provide your…

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Q: write the equation of the tangent and normal line line of the curve. huow soution your 2. (3.0) f…

A: First, check if the given point lies on the curve, f(x) . If the point is on the curve, then compute…

Q: 9. Find the equation of the line tangent to the curve y = 3x5 + 10x³ + 15x + 1 at its point of…

A: the given curve , y=3x5+10x3+15x+1 we have to find the equation of the tangent line to the given…

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² - 2x³ at the point where x = a

A: given,y=3+4x2-2x3

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² − 2x³ at the point where x = a -

A: The equation of the curve is given by y = 3+4x2-2x3 To evaluate: The slope of the tangent to the…

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

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Q: Determine the equation of the tangent to the curve y = x - e^-x that is parallel to the line 6x - 2y…

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Q: Find the equation of the tangent to the curve y=x²-x -2 at the point (1, -2).

A: We have to find the equation of the tangent to the curve y=x2-x-2 at the point (1,-2).

Q: Determine the equation of a tangent to the curve: y =. (x3 - 5x + 4)(3x2 - 2x) at the point (1,-2)

A: The given curve is y=x3-5x+43x2-2x at the point 1,-2.

Q: 1. Find the slope of the graph of the function f (x) = v3x + 4 at x = 7. Then find an equation of…

A: equation of tangent line is (y-y1) = slope (x-x1)

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

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Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

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Q: Find an equation for the line tangent to the graph of f at (2, 28), where f is given by f(x) = 5x³ –…

A: Given function is fx=5x3-5x2+8. To find an equation of tangent line to the graph at point 2,28.…

Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

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Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: Find the equation of the tangent line to the curve y=x4 -14x2+17x+40 and perpendicular to the line x…

A: The equation of given curve is   y=x4-14x2+17x+40  On differentiating with respect to x, we get…

Q: Find the equation of the line that is tangent to the curve y =-3e* at x = In 2. %3D

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Q: Find an equation of the line tangent to the curve defined by x^3+2xy+y^3=4 at the point (1,1).

A: To find the equation of the tangent line at the point (1, 1) to the curve given below.

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: Find an equation of the line tangent to the curve defined by x^3+6xy+y^5=21 at the point (2,1)

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Q: At what point (x,y) is the tangent line to the curve y=2x2-5x+8 parallel to the line y=3x-7

A: It is given that

Q: What is the equation of the tangent line to the curve f(x)= 4x2 + 2x -1 at the point x=0 ?  a.)…

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Q: Find f (4) and f ,(4) if the tangent line to the graph of f at x = 4 has equation y = 3x − 14.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.