Given that the line y= 2x +c is a tangent to the curve y = kx, where c and k are positive constants prove that k is a multiple of c.

Q: Suppose C=D0, so that 23 24y 5x3 = 0. Find all points (x,y) at which the tangent line to the…

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Q: If the slope of the tangent line to the graph of y%3f(x) at x-Da is m(a)%=D2a+1, and f(1)=5, then…

A: Given: If the slope of the tangent line to the graph of y=fx at x=a is ma=2a+1and f1=5. To Find: f2…

Q: Find the two possible values of a so that the tangent lines to f(x) = x3+2x2 and to g(x) = 8x-3x2 at…

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Q: The tangent line to y=f(x) at (2/(2) is line through given point whose slope is equal to (a) f (a)…

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Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Find all the value(s) of x at which f(x)=(7x^3/3)+3x^2−x+9 has a horizontal tangent line.

A: The values of x at which the given function has a horizontal tangent line can be found by evaluating…

Q: Show that the tangent lines to y = x – x2 at are parallel if a = b or a +b = 2. x = a and at x = b |

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Q: The product of all the values of x for which the tangent lines to the graph of y= are parallel to…

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Q: Given f(z) = x+ VE Calculate the tangent line at the point (16, 20) y : (2- 16) + 20

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Q: If the tangent line to y=f(x) at (4,3) passes through the point ( 0,2) , find f(4) ,f  '(4)

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Q: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

Q: Find a such that the tangent lines to y = x3 − 2x2 + x + 1 at x = a and x = a + 1 are parallel.

A: Consider the function: yx=x3-2x2+x+1 Slope of a tangent at any point of a function is given by…

Q: The tangent line to the curve il me f(a) at 2 m 1 goes through the points y=f(x) x == and Find the…

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Q: Show that if P lies on the intersection of the two curves x2 - y2 = c and xy = d (c, d constants),…

A: Given : The two curves x2 - y2 = c and xy = d intersect at point P where c and d are constants.…

Q: Show that if P lies on the intersection of the two curves x2 − y2 = c and xy = d (c, d constants),…

A: Solution:Givenx2-y2=c     and   xy=dTo prove tangent curve at P are…

Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: The tangent line to the graph of y = In(2x) is perpendicular to x + 4y = 1 at the point where…

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Q: Find the slope of the tangents to the curve at the points (P1 and P2) where it crosses the x-axis.…

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Q: Find the implicit equation of the tangent plane to z = In(x² + 1) + y² at the point (0, 4, 16).

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Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: Find a > 0 such that the tangent line to the graph of f (x) = x2e−x at x = a passes through the…

A: The tangent to curve at a point is a line that touches the curve at that point and with a slope…

Q: Find the equation of the tangent plane to z = e + x + x³ + 9 at the point (2, 0, 20). z =

A: According to question We have to calculate the equation of the tangent plane .

Q: Find a number a so that the tangent lines to y= x° + 11x +x + 13 at x = a and at x = a+ 1 are…

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Q: Given: f(x)=x2+2 find the equation of a line tangent at point P(1,3) using limits

A: To find the equation of a line tangent at point P(1,3) on below curve using limits.

Q: The equation of the tangent line to f(x) = In x at x = 1 is O y = x - 1 O y = x O x = 1

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Q: Determine the value of a, given that the line ax+y+1 = 0 is tangent to the graph of y= ax-6x+1 at x…

A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

Q: If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4). f(4)…

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Q: The tangent line to the graph of y = In(2x) is perpendicular to x + 4y = 1 at the point where…

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Q: a, given that the line ax+y+1 = 0 is tangent to the grapl

A: We have to find the value of a according to the given information

Q: Find all values of x for which the tangent line of f(x) = V x2 + 18x + 96 is horizontal.

A: Given that, the tangent line horizontal. That is it is parallel to x axis. The equation of the…

Q: If the tangent line to y = f(x) at (3, 2) passes through the point (0, 1), find (3) and r(3). (3) =…

A: In this question, we need to find f(3) and f'(3).

Q: If y-mx+B is thế équation of the tangent line to the curve X +2xy – y+ x = 39 at x=5 with a negative…

A: At x=5 we find y The points are (5, 1) and (5, 9)

Q: Find an equation of the tangent plane to the graph of f (x, y) = xy 2 - xy + 3x 3y at P = (l, 3).

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Q: Find an equation for the tangent line to the graph of f(x) = -2x2 + 2x + 3 at the point where x = 1…

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Q: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line a + y = -1 at the point…

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Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: 2i Find the eguation of the tangent: lime to tul Cur ve y=4x -x* at the point (l,3).

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Q: Given that the graph of J (X) passes through the point and that the slope of its tangent line at +…

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Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

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Q: If the Tangent line to y=f(x) at (1,2t pass through the point (0,3) Find l1) and f'(1) A. (1) = 0…

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Q: Given that the graph of f(x) passes through the point (6, 10) and that the slope of its tangent line…

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Q: If y1=2x+4 and y2 =x^2+C, find the value of C such that y2 is tangent to y1

A: Given: y1=2x+4    and    y2 =x²+C   To find :the value of C such that y2 is tangent to y1

Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

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Q: 22. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).…

A: #22 f(4) ? f'(4)?

Q: y = In(1 – a²) ; 0 < æs

A: Solution:-