Exercise 3: Consider the curve (x2+y2)2 = x2-y2. Find all the points on the curve with a horizontal tangent line, and all points on the curve with a vertical tangent line

Q: Find the equation of the tangent line to the curve y = 2xe^x at the point (0,0) in y = mx + b form m…

A: We have the given equation of the curve y=2xex   We have to find the equation of the tangent line…

Q: use implicit differentiation to find an equation of the tangent line to the ellipse at the given…

A: Using implicit differentiation you can find the derivative without separating the dependent variable…

Q: Construct a smooth curve tangent to the line segments starting at point P. P

A: Given: a group of line segments joining to form a zig-zag figure. Aim to form a curve which is…

Q: Find the equation of the tangent line to the curve y= (1+2x)2 at the point (2, 25). y = %3D

A: This question is based on application of Derivative.

Q: Find the tangent plane to the equation 5e*- öy at the point (12, 24, 5).

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Q: Show that there is a line that is simultaneously tangent to both the curves y = ex and y = lnx.

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Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: On the curve y3Dx2 ,find a point at which the tangent is parallel to the chord joining (0,0) and…

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Q: Find the slope of the tangent line to the curve 2x + 2xy + 2y = 32 %3D at the point (-4, 2).

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Q: find the equation of the tangent plane of this surface

A: In this question, we check the surface is simple and then we find the equation of tangent plane at…

Q: Explain how to find points on the curve x = f(t), y = g(t) at which there is a horizontal tangent…

A: Consider the following parametric curves. x=ft, y=gt Now, to find the tangent line at a point on…

Q: Assume every secant line of the curve y = f(x) has slope at least 3. Then every tangent line of the…

A: Given: Every secant line of the curve y=fx has a slope atleast 3.Then every tangent line of the…

Q: Find the equations of all tangent lines to the curve x² + 4y2 = 8 that pass through the %3D point…

A: The curve x2+4y2=8 that pass through the point (-4, 0). We have to find the equation of all tangent…

Q: Find the slope of the tangent line to the curve -2x^2-3xy-3y^3 = -246` %3D at the point `( 3,4).…

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Q: Find the slope of the tangent line to the curve (a lemniscate) 2(x² + y²)° = 25(a² – y²) at the…

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Q: Find the slope of the tangent line to the curve - 3x + lay+ 3y = 199 | %3D | at the point (1, – 4).

A: We are given a curve and we need to find out the slope to the tangent line at the point (1,-4). For…

Q: Find the equation of the tangent line to the curve y = IVa at the point (16, 64). %3D y =

A: The standard form of the tangent line helps to find the required equation of the line. The standard…

Q: x = e' and y = te %3D

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Q: Use the guidelines of curve sketching to sketch the curve y = 1-x2 %3D

A: Given: y=x1-x2

Q: In Exercises 25-34, find an equation of the tangent line at the point speci- fied.

A: y=cscx-cotx We need to find the equation of the tangent line at x=π4

Q: sketch the curve ƒ(x, y) = c, together with ∇ƒand the tangent line at the given point. Then write an…

A: sketch the graph of x2-xy+y2=7

Q: Let f(r, y) = - (5x² + 4xy+ y²). Then an implicit equation for the tangent plane to the graph of f…

A: Given function is, fx,y=−5x2+4xy+y2 To find the implicit equation of tangent plane to the graph of f…

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: 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: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: m 10. PREVIEW ONLY -- Find an equation of the tangent line to the curve y = 9° at the point (1,9).…

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Q: Find an equation of the tangent line to the curve x2+y+y2=13 at the point (-1,3)

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Q: Find the slope of the tangent line to the curve 3x + læy + 3y° = - 199 %3D at the point (1, – 4).

A: we know that the slope of the tangent to the given curve is =dy/dx.

Q: Find the point (xo, yo) on the graph of y = x³ + 3x? + 8x – 3, at which the slope of the tangent…

A: To find the slope of the function we need y'y=x3+3x2+8x-3y'=3x2+6x+8

Q: Determine the tangent line(s), in standard form, to the curve y = (x- + 1) (x – 9) that are…

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Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

Q: Consider the curve x²y + y2x = 6 %3D Find the coordinates of the point (x,y) where the curve has a…

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Q: Make the curve y=ax³ +bx²+cx+d pass though (0,3) and have at (1,2) a point of inflection with a…

A: Given: T curve y=ax3+bx2+cx+d passes through the point (0, 3). The point of inflection is (1, 2)…

Q: Find the slope of the tangent line to the curve -3x2 +3xy- 4y = - 247 %3D at the point (1, 4).

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Q: Use implicit differentiation to find an equation of the tangent line to the ellipse defined by…

A: topic-  tangent lines

Q: 2. Use the guidelines to sketch the curve. Y In x x²

A: The given function is: y=ln xx2 Note that the domain of the function is (0,∞). First of all, let's…

Q: At what point is the tangent line to the curve y³ : = 6x² perpendicular to the line 2x + y = 2 = 0?…

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Q: Show that th equation of the tangent to the curve X 1승 +1-2(a 0,b + 0) at the point (a,.b) is 즈+-2 X…

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Q: Sketch the line tangent to f at the point corresponding to x = -1. Label it as T.

A: d) The tangent to the given function at x=-1 is as given in the following figure.

Q: Show that the line y = mx + b is its own tangent line at any point (x0, mx0 + b).

A: Given:Show that the line y = mx + b is its own tangent line at any point (x0, mx0 + b).

Q: Find the tangent lines to curve x² + 2y2 = 9 that is perpendicular to line 4x – y = 6? %3D

A: Given the equation of line is 4x-y=6.   Rewrite the equation in slope intercept form. y=4x-6   Thus,…

Q: Find an equation of the tangent plane at the given point. z = In(x-2y), (3,1,0)

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Q: Find the family of curves in the plane such that in each point P(x,y) of it, the intercept of its…

A: Write the equation of the tangent for the family of curves for any point P (x , y). Assume the slope…

Q: Use implicit differentiation to find an equation of the tangent line to the ellipse      x2/2 + y2/8…

A: Given, x22+y28=1                              ...(1) Point (1, 2)

Q: Find the equation of the line tangent to the curve 2(z² + y°)* = 25(z² – y²) at the point (3, 1).…

A: Suppose a line passing through with slope  m then equation of line is .