Write the equations of the lines tangent to the curve y x- 4x at both a 0 and a 2. Then, determine the point of intersection for these two tangent lines.

Q: C. Find the slope and the equation of the tangent line to the curve. 1. у %3D х2- 4х + 1 at (2, -3)

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Q: . Find the lines that are tangent and normal to the curve at the given point x² + y? = y* - 2x,…

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Q: Find the equation of the line tangent to the curve y = 3x?(x² – 6x) at x = 2.

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Q: Find the equations of both lines that are tangent to the curve y = x - 3x2 + 3x - 3 and are parallel…

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

A: y2-x2+6x-13=0 --------------(1) Differentiating with respect to x ddxy2-x2+6x-13=ddx(0)…

Q: Determine the equation, in y= mx + b form, of the line that is perpendicular to the slope of the…

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Q: Write the equation of the line tangent to the graph of y = x3 at the point where x = -1.

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Q: Find the slope and equation of the tangent line for the equation 5.x'y – 6y° = 7x² – 35 at (1,2).

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Q: Find an equation of the line tangent to the given curve at a. y = x3 – 4x2 + 2x – 1; a = 2

A: Slope m of the tangent will be given by dydx Therefore, dydx=ddxx3-4x2+2x-1 ⇒dydx=3x2-8x+x…

Q: find the equation of the line tangent to the curve at the given point x2y2=4y ;(2,1)

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Q: Find the slopes and equations of the lines tangent to y = f(x) at the given point.

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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 the equation of the line segment tangent to the curve y−2x2−1=0y−2x2−1=0 which is parallel to…

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given curve is The point (-1,3) lies on the curve if it satisfies the equation of curve Therefore,…

Q: Find the equation of the line segment tangent to the curve y−2x^2−1=0 which is parallel to the line…

A: Given curve is y-2x2-1 = 0

Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

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Q: find the slope of the curve at the point indicated y = 1/x - 1, x = 3

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Q: Find an equation for a line that is tangent to the graph of y = ex andgoes through the origin.

A: To find the equation of a line that is tangent to the graph of y=ex and passing through origin.…

Q: Write the equation for the curve that has slope of 2y/x for each point P(x,y) on it and passes…

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Q: Find the equations of all lines through the origin that are tangent to the curve y = x³ – 4x? – 4x.…

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Q: Find the equation of the tangent line to the circle at the point (-3, -4). Equation of the circle *…

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Q: Determine the equation of the tangent to y = (x – 7)(x+2) at the point P(-1,-8). Answer:

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Q: Determine the equation of the curve for which the tangent line at every point has a slope of 25, x =…

A: Topic = Coordinate geometry Correct option = D

Q: Determine the equation of the line tangent to the curve   at the point (-1,1) and reestablish a…

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Q: Write the equation of the line tangent to the graph of y = 5xe*+4 at x = 1. a) y = 5e-1+4 b) y =…

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Q: Verify that the given point is on the curve and find the lines that are a. tangent and b. normal to…

A: Substitute the point (-3,-1) in the given equation.

Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Given: xy+2x-5y=2; 3,2 for finding equation of tangent, we need to find slopem1 of tangent  we know…

Q: Show At what points does the equation of the line tangent to the curve y=1/x+3 have a slope equal to…

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Q: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 25x2 +…

A: 16y2+200x-160y+400=0 Differentiating with respect to x implicitly 50x+32ydydx+200-160dydx+0=0…

Q: Find the slope of the curve at the given point. y3= x3/2a-x   at (a,a)

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Q: how do you find the equation of the tangent line at the given point on each curve? x2+ y2=25 ,…

A: To determine the equation of the tangent line, the slope of the curve at the given point is to be…

Q: Consider the following curve. y = 2x2 - 10x + 1 Find the slope m of the tangent line at the point…

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Q: Find the slope of the tangent line to the curve - l2? – 2ay + 4y³ = - 249 at the point (1, – 4).

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Q: 2x at x =1 y = Зх-1

A: Find dydx as follows. y=2x23x-1dydx=22x3x-1-3x23x-12dydx=23x2-2x3x-12 Find dydx at x=1 as follows.…

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

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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: Determine the equation of the curve whose slope at any point is equal to and which passes through…

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Q: Determine the equation of the line tangent to the graph of y when x = 9. 2 + VI

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Q: What is the slope of the tangent line to the graph of y = x3 – 4x + 2 at point (2, 2)? %3D А. 1 В. 4…

A: Given function, y=x3-4x+2Diferentiate w.r.t.…

Q: Find the equation of the tangent to the curve y 18x- 2y-3 0. 3e3 that is parallel to the line

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Q: Determine the equation of the tangent to the graph of the equation xy – 2x'y-3ry + 5y – 4 = 0 at the…

A: To find the equation of tangent to the given equation at (1,2).

Q: Find an equation of the line that is tangent to the graph of fand parallel to the given line.…

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Q: Determine the equation of the line parallel to y+1=0 and tangent to y = 3x – 5x + 4 -

A: Recall that the slope of the parallel lines is equal. And the slope of the tangent line at any point…

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,

Q: The equation of the line that is tangent to the curve y=2x3−6x and is perpendicular to 18y+x+3=0…

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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.