If f(x) = 8x - x³, find f'(1) and use it to find an equation of the tangent line to the curve y = 8x x' at the point (1, 7).

Q: 2. Find the slope of the tangent line to the curve y = x3 – 2x + 1 at x = 1.

A: As we know that: The first derivative of the function at a point is equal to the slope of the…

Q: Find the equation of the tangent line to the curve y = 8 ln(x – 63) at the point (4,0). y =

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Q: 4. Find the equation of the tangent line to the curve y=x-2x+3 at the point (2,3).

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Q: Find the equation of the tangent line at the given value of x on the curve. y° +xy² -61=x+3y°; x:…

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Q: Find the equation of the line tangent to the curve y = ex/x at x=1

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Q: Find an equation of the tangent line to y = xt + 2x2 – x at x = 2

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Q: Find the equation of the tangent line to the curve y = x Vx +5 at the point (2,6).

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Q: 3. Determine the slope of the tangent line to the curve f(x) = at (2x + 1)2 x = 1 by using the…

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Q: Find the equation of the tangent line at the given value of x on the curve. 2y' +xy - y = 54x*, x= 1…

A: Explanation: Given that: 2y3+xy-y=54x4 x=1 Concept: The standard equation of tangent line y=mx+c…

Q: Find equation of the tangent line to the curve y = v2x + 1 at the point (4,3).

A: Given:    y = √(2x+1)  Point (4,3)

Q: 3. Find the equation of the tangent line to the curve y = x³ at x=1.

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Q: π Find the equation of the tangent line to the curve y= Jx² –sin-(4x) at x =-. 4

A: We are given the equation, y=x2-sin24x at x=π4. Here,           dydx=x2-sin24x'…

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + ly 38 - at the point (1, – 3).

A: Given:   To determine: Slope of the tangent line to the given curve at point (1, -3)

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

A: Given: y=ln(x2-3x+1), (3, 0)

Q: Find the point where the tangent line to y=x2 at x=0.4 crosses the x-axis. x-intercept =

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Q: 2. Use implicit differentiation to find an equation of the tangent line to the curve z2+2ry-y²+x = 2…

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Q: Find the slope of the tangent line to the curve of y = x 2 at the point where x = −6

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: Find an equation of the tangent line to the curve at thegiven point  y = ln ( x 2- 3x + 1 )       ,…

A: Given,y = ln (x2-3x+1)slope of tangent line is equal to the first derivative of curve at given point

Q: Find the point where the tangent line to y = x* at x 0.3 crosses the x-axis. x-intercept =

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Q: Determine the equation of the tangent line to the curve y = f2 (x) at x = −2con

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Q: y = 16 X + x² at x at x = 4.

A: Given Equation :- y=16x+x2  Find the equation for the tangent line to the curve at x=4

Q: Find the equation of the tangent line to the curve f(x)=x9 ln(x2) at x = e. (Do not approximate)

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Q: Find an equation of the tangent line to the curve at the point (1, y = x4e-x

A: Given that      y = x4e-x We have to find an equation of the tangent line to the curve at the point…

Q: Find the equation of the tangent line to the curve x4+y4=2 at the point (1,1)

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Q: Find the equation of the tangent line at the given value of x on the curve. 2y (x-4) +x/y = 8; x=4 y…

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Q: The slope of the tangent line to the curve x^3 + y^3 = 6xy at the point (3,3) is

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Q: Find the equation of the tangent line to the curve y sin(sin x) at the point (7,0).

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Q: (a) Find the equation of the tangent line to the curve y = 2lnx at x = 5.

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: Determine the equation of the tangent line to the curve, y = 4x e at x = 1. Use exact values.

A: Given y=e4xx3     at x=1To find equation of tangent:

Q: Find the slope of the tangent to the curve y= 2 sin'x at x-

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Q: Find the equation of the tangent line to the curve y = 4r- 3r through the point r= 2 using the…

A: Given curvey=4x-3x2

Q: Find the equation of the tangent line to the curve y=x4 at the point (−1,1).

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Q: Find the equation for the tangent line to the curve y = 25 X + x² at x = 5.

A: Equation of tangent line to a curve y=f(x)  at x=a is given by y-f(a)=f'(a)(x-a)

Q: Find the equation of a tangent line to the curve y=xe2x at the point where x=1

A: We need to find the equation of a tangent line to the curve y=xe2x at the point where x=1. Now,…

Q: Find the slope of the tangent line to the curve - 2x2 + 2xy – 4y³ = 0 at the point (1, – 1). -

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Q: Find the equation of the tangent line at the given point on the curve. 109y2e 327x/10. (10,3) , 3x2…

A: Given,

Q: Find an equation for the tangent line Y= 4x-since when x=0

A: To find the equation of tangent  line

Q: Find the slope of the tangent line to the curve x + xy – y = 23 at the point ( – 3, – 2). -

A: The given function is x2+xy-y3=23 The point is x0,y0=-3,-2

Q: Find the tangent line to the curve y = 2x - x2 at (2,0)

A: The equation of the curve is given by y = 2x-x2 The point is x0, y0 = 2, 0 Formula Used: The formula…

Q: f(x) = ln(x − 1) at x = 2

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Q: Find the slope of the line tangent to the curve y = sin' x at the point where x-x/3

A: We have to find the slope

Q: Find the slope of the line tangent to the curve y = sin x at the point where x = 3

A: Given: y=sin5x To find: The slope of the line tangent to the curve y=sin5x at the point where x=π3

Q: What is the equation of the tangent line at x=-2 of f(x)=√√x -1

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Q: Find the equation of the tangent line to the function y = sec'x at the point :2 4-

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Q: Find the tangent line to y = √(x2 - x + 7) at x = 2.

A: Differentiating with respect to x, we get

Q: The slope of the tangent line to the curve y=2e10xcos(-6x) at x-0 is

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Q: . Find the equation of the tangent line to the curve y =1 – 2x + x² at (1, 2).

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Q: Find the equation of the tangent line to the curve y = x* + 6e* at the point (0, 6). y =

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Q: x =t - sint y = 1- cost

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