At what point of the curve y = x3 + 3x are the values of y’ and y” equal?

Q: Find equations of the tangent line and normal line to the curve at the given point. yy = √xx xx+1 at…

A: According to the given information, it is required to determine the equation of tangent and normal…

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 an equation for the line in the xy-plane that is tangent and normal to the curve x³y² + y² = x…

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Q: 8. Find the equation of the tangent and normal to the curve y = x3 3x + 1 at x = -1. [4] -

A: We have to find the eqution of tangent and normal of given curve y

Q: Find an equation of tangent line at the point (−1, 1) to the curve x^4y^2 + 1 = x^2 + y^3

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the equation of the tangent line to the curve y²(y² – 4) = x² (x² – 5) at the point (0, –2). |

A: Equation of tangent line is given by:y-y1=dydxx=x1·(x-x1)      .............[1]So first find dydx at…

Q: The equation of the tangent line to the curve x2 + y = 9, at (6,-16) is %3| 16 y = (x + 6) – 16 6 6…

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Q: The Normal to the curve 2x² – y² = 1 at the point (1,1)

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Q: Find an equation of the tangent line to the curve y= (1+2x)^10  , (0,1)

A: First find the derivative of the curve at given point than write the slope intercept form of…

Q: 3. Find the slope of the tangent line to curve x=2sin2t, y = cos4t when t=-

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Q: Find an equation of the tangent line to the curve at the given point. у %3D sec(x), (л/3, 2) 2nv3 y…

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Q: At how many different values of x does the curve y = x +2x have a tangent line parallel to the line…

A: Given equation of curve is Differentiating with respect to x, we get

Q: Find an equation of the line tangent to the curve defined by x + 3xy+ y = 5 at the point (1, 1).

A: Given  Curve ia x3 + 3xy + y2 =5 at the point(1,1) Find equation of tangent.

Q: At how many different values of x does the curve y =x+ 2x have a tangent line parallel to the line…

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Q: Find the equation of the tangent line to the curve y=5x²-1 at x= -1. Y=15x + 9 Y=15x-6 O y= x-6 O…

A: Topic:- application of derivatives

Q: Find equations of the tangent lines to the curve y = x-1/x+1 that are parallel to the line x − 2y =…

A: Given,        The equations of the tangent lines to the curve y=x-1x+1 that are parallel to the…

Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

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: Determine the equation of the line tangent to x² + sin y = xy² +1 at the point (1,0).

A: The equation x2+siny=xy2+1, we have to determine the line of the tangent at the point (1,0).

Q: 1) Find the equation of the tangent line to the curve: x* + xy – y = 7 at (3,2) %3D

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Q: ind the slope of the tangent line to the curve y = V4x – 3 at the point (13, 7).

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Q: Find the equation (in terms of x and y) of the tangent line to the curve r=4sin2θ at θ=π/3. y=?

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Q: Find an equation of the line tangent to y = xsin x at the point x = 1.

A: The given equation is y=xsinx.

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

A: Here, to find the equation of the curve of the form y=f(x) with x-intercept 2. That is curve passes…

Q: Calculate the equation of the tangent line to the curve 2r³ + xy +3x+ y = 2 at the point (0, 2).

A: To find the equation of a tangent line to the given curve at point (0,2).

Q: Find an equation of the tangent line to the curve at thegiven point.

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Q: 24)) Since the tangent of the curve y = x ^ 5 + ax - 3 at the point x = 1 is y = x -b, then b =?

A: Given that y=x-b is the tangent of the curve y=x5+ax-3 at the point x=1.

Q: Find the equation of the tangent to y-cos 2x at the point 0. Oal y--2- Ob) y- 2x+ O) y--+1 O d)…

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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: 3 at the point ( 6, (0.) The slope of the tangent line to the curve y = is:

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Q: 2xy - y² + x = 2 at the point (1,2). - Find the equation of the tangent line to ² +2

A: By using equation of tangent line formula, we find the required tangent line.

Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: Find equations of the tangent and normal line to the curve y = V3 +x² at x = 1.

A: Recall: slope-point intercept form: y-y1=m(x-x1) ; where 'm' is the slope and (x1,y1) given points.…

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

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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 equation of a curve in the xy-plane that passes through (1,3) and -6x(2+y) V3 – 3x2 whose…

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: Find equations of the tangent and normal line to the curve y (2x+1) %3D at x=2. (3x2-2)

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Q: Find equations of the tangent lines to the curve at the given point: f(x, y) = 4x2+y? 2

A: Given:      fx,y=4x2+y2 at 32,1          4x2+y2=0            y2=-4x2 differentiating on both sides…

Q: Find an equation of the line tangent to the curve defined by x^3+2xy+y^3=4 at the point (1,1).

A: To find the equation of the tangent line at the point (1, 1) to the curve given below.

Q: Find the equation of the tangent line to the curve y= x4 + 6ex at the point (0,6). Enter exact…

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Q: Find the equation of the line tangent to the curve y=x+cosx at the point (0,1)

A: Given, curve and point

Q: Which is the equation of the tangent line to the curve x* +xy = 4 + y at the point (4,6)?

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Q: Find the equation of the tangent line to the curve y = + 6x at its point of intersection with the…

A: The tangent of any given function is the line that touches the curve of the function at only one…

Q: Find the equation of the line tangent to the curve xy3+xy=20 at the point (10,1). When the equation…

A: It is given that, the equation of the curve is xy3 + xy  = 20. Use implicit differentiation to…

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 .