Make the curve y = ax4 + bx3 + cx2 + dx + e pass through the points (0,3) and (-2,7) and at (1,4) have a point of inflection with a horizontal tangent line.

Q: Make the curve y=ax*+bx³+ cx²+ dx+e pass through the points (0,3) and (-2,7) and at (1,4) have a…

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Q: 19. Does the line that is tangent to the curve y = x3 at the point (1, 1) intersect the curve at any…

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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: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

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Q: Find all equations of the tangent line to the common curve of the two surfaces with equations z = x²…

A: follow next step

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: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: Find the orthogonal trajectories of the family of curves y = ax² + 4ax + 4a, where a being…

A: Orthogonal trajectory: If a curve cuts every member of a given family of curves at right angle, then…

Q: 2. Find the equation of the tangent plane to the surface z = 3++ at point (-4, 3).

A: Topic- application of derivatives  Tangent to surface

Q: Find an equation of the form y = f(r) for a curve with z-intercept 2 whose tangent line at any point…

A: we have to find an equation of the form y=f(x) for a curve with x-intercept 2 whose tangent line at…

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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Q: Find the equation of the tangent line to the curve y = (5 In(x))/x at the points (1, 0) and (e,…

A: Formula of equation of tangent is y-y1 = m(x-x1)

Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

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Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: The slope of the tangent line to the curve y = 4/x at the point (3, 4/3) is: Must be written in y =…

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Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Find the tangent and normal line to the curve at the specified condition. 12x2 - 20y2 = 55 parallel…

A: Given that the curve is 12x2-20y2=55 and the required tangent and normal line is parallel to the…

Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: Find an equation for the tangent line to the curve y = xV 2x² - 14 at the point (3,6). O y- 6 = 14(x…

A: The equation of the tangent line to the curve is, y - 6 = 11(x - 3)  The detailed solution is as…

Q: 3. Determine the equation of the tangent plane and normal line to 2xz + y²z³ = x + 5 at (1,0,3)

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Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

A: x=13yy-3,   1≤y≤9 Differentiating with respect to y, we get…

Q: Find the equation of the tangent line to the curve y = 2 In(x - 26) at the point (3,0). %3D y =

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Q: Find the equation in terms of x and y of the tangent line to the curve r= 4sin 5θ and θ =π/3.

A: Given: r=4sin5θ  and θ=π3

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 7z2 = 27,   (−3,…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Find the point (xo, yo) on the graph of y = x + 9x2 + 3x - 4, at which the slope of the tangent line…

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Q: Find the equation of the tangent line at the given point on the curve. 3y-x = 8, (16,2) %3D

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Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: Find the tangent and normal line to the curve at the specified condition.  3x3 - x2 - 12x + 6 at…

A: Suppose we wish to find the equation of the tangent tof(x) = 3x3 − x2 - 12x +6 the points where the…

Q: Find the points on the curve y=2x^3 + 3x^2 -12x +3 where the tangent line is horizontal.   (x,y) =…

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Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.!

Q: Find an equation of the tangent plane to the surface at the given point. x² + y² 7z² = 138, (-8, -9,…

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Q: The 50 g bullet travelling at 100 ms-1 strikes the 2 kg block centrally and is embedded within it.…

A: Please check step 2 for the solution.

Q: A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane…

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

A: Given curvex2+4y2=8Differentiate above curve w.r.t…

Q: Find the orthogonal trajectory of the curve x^2 + y^2 = 2 ln x

A: See the details solution in below

Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

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Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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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: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

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Q: Find all​ x-coordinates of points​ (x,y) on the curve y=(x−2)4(x−5)-3 where the tangent line is…

A: Given,          y=x-24x-5-3 where the tangent line is horizontal.

Q: A) Determine the equation of the tangent line to the curve xsin(y) – x²cos(y) = 1 at the point (1,4)

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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 .

Q: Calculate the gradient of the tangent line to the curve y3 - x3 -xy = 1at the point (-1,0).

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