Prove that the curves y=f(x),(f(x)>0) and y = f (x)sin x, where f(x) is differentiability function, have common tangents at common points.

Q: find an equation of the tangent plane at the given point. f (x, y) = ln(4x2 − y2), (1, 1)

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Q: (a) Differentiate with respect to x: g(x) = 4x2 – x +5 (b) Differentiate with respect to x: h(x) =…

A: We know that :ddxf(g(x))=f'(g(x))g'(x)

Q: Find all value of x=c, so that the tangent line to the graph of f(x) at (c,f(c)) will be horizontal…

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Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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Q: Find the slope of the tangent line to the curve of intersection of graph of f and the plane x =2 at…

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Q: tangents are drawn from the origin to the curve y=sin x.Prove that their points of contact lie on…

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Q: Find all points (x,y) on the graph of y = X-4 with tangent lines perpendicular to the line y = 4x-…

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Q: Find an equation of the tangent line to the curve at the given point. y = In(x² – 6x + 1), (6, 0) y…

A: As per guidelines we have to solve one question Please repost other questions again

Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

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Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: Find all points (x,y) on the graph of y = X-4 with tangent lines perpendicular to the line y = 4x-3.

A: The graph of y=xx-4 with tangent line perpendicular to the line y=4x-3

Q: Tangents are drawn from the origin to the curbe y=sin x.Prove that their points of contact lie on…

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Q: Tangents are drawn from the origin to the curbe y = sin x.Prove that their points of contact lie on…

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Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

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Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: prove that the curve y = f(x),(Ax) >0) and y = (x)sin x ,where fx) is differentiable function ,have…

A: We use the Given Curves, Prove that have a common tangent at common point.

Q: Find the​ x-coordinates of all points on the curve y = (-x^2+4x−3)^3 with a horizontal tangent…

A: We know the slope of the tangent where it is horizontal is 0. we will need to find the derivative of…

Q: Show that the inflection points of the curve y=sinxxy=sin⁡x/x lie on the curve y2(x4+4)=4.

A: Given: To prove that the inflection points of the curve y=sinx/x lie on the curve y2(x4+4)=4.

Q: , If the curves yı = -x² + ax +b and y2 x² + cx - 2 have the common tangent line at the point P(1,2)…

A: Given information: There are two equations  are y1=-x2+ax+b, y2=x2+cx-2 have a common tangent line…

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

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Q: Let f(x) = (x - 12) / (2x + 6) Find an equation for the tangent line to the graph of f at x = 2 y =…

A: We find f'(x) first using quotient rule

Q: Prove that f (x) = x3 − 12x is differentiable. Compute f'(x) and findan equation of the tangent line…

A: For a function f(x) to be differentiable the limit limh→0f(x+h)-f(x)h must exist. This limit is…

Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: Show that the tangent lines to the curve y = (π sin x)/x at x = π and x = -π intersect at right…

A: The equation of the curve is y=πsinxx

Q: 1. (a) Use implicit differentiation to find the slope of the tangent to the curve y? – xy +y + 2 = 0…

A: Given: The equation of the curve y2-xy+y+2=0

Q: Find an equation of the tangent line to the curve at the giv y = In(x2 - 3x + 1), (3, 0) y =

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Q: x2y2=x2-y2

A: Using method to find locus we get

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: Find the equation of the tangent line to the curve y = f(x) at the given point. y = f(x) = x²-x, at…

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Q: Find all points (x, y) on the graph of y = x/(x - 2) with tangent lines perpendicular to the line y…

A: Given:

Q: Find a point on the curve y=x2−2x−3 at which the tangent is parallel to the x−axis.

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Q: Find the equation of the tangent line on the curve defined by 2xy- y² =1 at x = 1. A y=x-1 B y=1 ©…

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Q: Show that the tangent lines to the curve y = (paisin x)/x at x = pai and x = -pai intersect at right…

A: y=π sinxx Differentiating with respect to x, we get dydx=ddxπ…

Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the line y= 4x - 3.…

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Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Determine the points in the interval [0, 2π) at which the graph of the function f(x) = √2x + 2…

A: We find point of tangent on given curve.

Q: Find the equation for the tangent line to the curve f(x)=cos(x)-2sin(x) at the point (0,1). O y=-x+1…

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Q: B - Find the point on the curve y = x3 + x2- 1 where the tangent parallel to the x- axis.

A: Topic- slope of tangent and application of derivatives

Q: Find the equation of the tangent plane to the graph of f(x, y) =−3x2 − y3 at the point (x, y) = (2,…

A: The given function is

Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the (x- 6) line y= 6x…

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Q: Find all points (x, y) on the graph of f(x) = x° - 5x + 26x + 19 with tangent lines parallel to the…

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Q: Find the tangent line to the graph of x (x² +y² ) = y² at the point

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Q: Find the slope of the tangent line to x2y2+x sin (15y) = 4 at any point, (x,y) on the curve.

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Q: Find the equation of the tangent line to the curve y = (2 In(x))/x at the points (1, 0) and (e,…

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Q: Let f(x) 2.x2. Then f'(x) = 4.x. Find the equation of the tangent li at x = 1 for f (x). That is,…

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Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1 What…

A: equation of tangent is y=4x-5 therefore equation of curve whose tangent is y=4x-5 ,…

Q: Find the equation of the tangent line to the curvef (x) = 2x³ 3. - x at x = 2. o T(x) = 14 – 23(x –…

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Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: Find the equation of the tangent line to the curve f(x)=5-x² at x = 2. O x-4y-2=0 O 4x + y +7=0 O 4x…

A: Find the equation of the tangent line to the curve f(x) =5-x^2 at x=2.