1 Find the x-coordinates of all points on the curve y = 12x* – 80x° - 144x + 29x + 26 where the tangent line is perpendicular to the straight line y = - -x + 5. 29 List all the x-coordinates. (Simplify your answer. Use a comma to separate answers as needed.)

Q: Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the…

A: Given: y=x2

Q: 2. Find the equations of tangents that can be drawn from the origin to the circle x² +y-2x+8y+2=0.

A: Given below the detailed solution

Q: B) Find all the points on the curve y=tan x, -n/2<x</2, where the tangent line is parallel to the…

A:

Q: Find the equation of the tangent plane to the graph of (x, y) = In (16x? – 13y²) at the point (1,…

A: We will find the first order partial derivatives fx and fy and then use the formula for tangent…

Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.

A:

Q: Find the length of the following curve. y = 2x + 4 on 3-2, 24 (Use calculus.)

A:

Q: 2/7 Solve for x. Assume that lines which appear to be tangent are tangent. SHOW YOUR WORK! 9x-2 8x

A:

Q: 98. Find the points on the graph of y = 2x6 – x* - 2 at which the tangent line is horizontal.

A: Find the points on the graph of  y=2x6-x4-2at which the tangent line is horizontal.

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: 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). :-

A:

Q: 1 Find the x-coordinates of all points on the curve y= 9x* – 48x° – 90x + 9x + 34 where the tangent…

A:

Q: The curves f(x) = x² + 2x + 5 and g(x) intersect at the point (– 2, 5). - x + 3 Find the acute angle…

A: Given that ,  fx=x2+2x+5  and ,  gx=-x+3 To find : the acute angle of intersection of curves. The…

Q: 8. The line y = -4x + b is tangent to the curve f(x) = 2x² – 8x + 12. Determine the value of b. %3D

A: The equation of the tangent at a point h,k on a curve y=f(x) is given by, y-k=f'(h) (x-h)

Q: 13. Find the equations of both lines that pass through the point (2, – 3) and are tangent to the…

A: We need to find equations of tangent lines.

Q: Draw a diagram to show that there are two tangent lines to the parabola y = x² that pass through the…

A:

Q: Find the length of the curve y = In (1 – 2*) over the interval [-,].

A:

Q: Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

A:

Q: Find the slope of the tangent line to the curve 12(2 + )? = 625(x² – }) (a lemniscate) at the point…

A: Slope of tangent line is the first derivative of given curve at point ( x , y ) . Slope = dy / dx…

Q: The slope of the tangent line to the parabola y 2x2 + 2x + 4 at the point (0, 4) = The equation of…

A:

Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

A:

Q: + 6) 2. Find the points where the tangent is parallel to x-axis, y =(x - 3a

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Q: Draw a diagram to show that there are two tangent lines to the parabola of  y = x2  that pass…

A: Given the parabola : y=x2Tangent passes through the point 0,-9 We need to find the coordinates of…

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: 7. Find the length of the curve y= x'+ I from x = 1 to x . 12x Give your answer as a simplified…

A:

Q: 3 Find the x-coordinates of all points on the curve y = (-x² + 8x – 7)° with a horizontal tangent…

A:

Q: A curve like Y = is called a serpentine. 1+2x2 3 n equation of the tangent line to this curve at the…

A:

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

A:

Q: Find a value for x so that distance from (x,3,6) to the origin is 9

A:

Q: The curves f(x) = x² + x + 4 and g(x) = - 5x + 20 intersect at the point (2, 10) Find the acute…

A: Given, fx = x2+x+4  and  gx = -5x+20  intersected at the point  2, 10 We have to find the acute…

Q: Find the equation of the tangent plane to the graph of f(x, y) = 2xy² + 2x³y? at the point (-1,2).…

A: To find the equation of a tangent plane.

Q: 5 Find the equation of line tangent the circle x+y = 25 at point (3, -4). .2 %3D

A:

Q: Find the length of the curve x2 1 In(1 – x) 2 4 1 between x = 0 and x 2

A: Recall: Length of the curve y=f(x) is given by on the interval a,b is…

Q: 5. How many lines are tangent to both of the parabolas y = -1-x² and y = 1+ x?? Find the exact…

A:

Q: Find the equation of the tangent plane to the graph of f(x, v) = In (17x² – 14y²) %3D at the point…

A: The given function is f(x,y)=ln17x2-14y2 and the point is 1,1. The equation of the tangent to the…

Q: 3 where do the curve of y = cosx and y = x³ -1 intersect?

A:

Q: (х — 3)4 Find all x-coordinates of points (x,y) on the curve y =. (x - 8)8 where the tangent line is…

A: If you like the solution then please give it a thumbs up... The Answer is:          x = 3 , -2

Q: find the slope of the curve at the point indicated. 19. у %3D 5x — Зх?, X =

A:

Q: (a) Find the equation of the tangent plane to the graph of : = (1,-1,5). + ) +4 at

A:

Q: How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what…

A: Given: The equations of circle are given as, Consider the parametric co-ordinates for the Eq. (A)…

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

A:

Q: Draw a diagram to show that there are two tangent lines to the parabola of y = x? that pass through…

A: NOTE: Refresh your page if you can't see any equations. . to find the slope of the tangent line,…

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

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 8) Find the slope of the tangent line to the graph at the given point. (x? - y)? = 4x²y - 3x - y,…

A: The slope of a tangent line to a curve is the differentiation of curve with respect to x at a given…

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: 25) Find the point on the curve y = Inx that is closest to the point (2, 3) with two digits accuracy…

A: So the point (2.731,1.0046) are closest to the curve y = ln (x)

Q: The curves f(x) = x² – 2æ – 5 and g(x) = 4x – 10 intersect at the point (1,-6). Find the acute angle…

A: Given data: The expression for first function is f(x)=x2-2x-5. The expression for the second…

Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.