(a) If F(x) = x2 - 5x, find F'(5) and use it to find an equation of the tangent line to the curve y = x² – 5x at the point (5, 0). F'(5) = y(x) (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. y y 20 20 10 10 F(x) F(x) -10 10 - 10 10 y(x) - 10 -10 -20 -20 y(x) y y 20 20

Q: Find an equation of the tangent line to the graph of y = ln (x^2) at the point (4, ln (16))

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Q: 2. Determine an equation for the tangent line to f(x) = x(x² + 1)3 at x = -1.

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Q: 3. Find an equation of the tangent line to the graph of y = log,x at the point ( 32,5).

A: We need to find the equation of the tangent line to the graph of y=log2x at the point (32,5) . Using…

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: 1. Find the equation of the tangent and normal line to the curve f(x) =x' - 3x +2 at (1, 0).

A: Given the function f(x) :

Q: 7. Find the points on the curve y=-x where the tangent line is parallel to the line y= 3x

A: The points on the curve y=x33-x where the tangent line is parallel to the line y=3x

Q: 1. Find an equation of the tangent line to the curve  x^2 + y +y^2 = 13 at the point (-1, 3). ?

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Q: 2. Find the equation of the tangent line to the curve y = x² – 2x - 3 that is parallel to the line x…

A: Given: The tangent line to the curve y=x2-2x-3 is parallel to the line x+y=1. To Find: The equation…

Q: 4. Find the equation of the tangent line to the curve y = 5x– 6/x at the point (1, –1).

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Q: 1. Find the derivative. g(x)=(4x-2)^5-√(x^2+8)

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: The slope of the tangent line to the curve y^2 = 5x – 1 at P(1, 2).

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Q: (b) Find the equation of the tangent line to the graph of the equation sin-"(x + y) = ;r² 2 at the…

A: Topic = Derivative

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: 3. Find the equation of the tangent line to the curve y = x2 - 3x + 4 that perpendicular to the line…

A: we have to find the equation of the tangent line to the curve y=x2-3x+4 that is perpendicular to the…

Q: 3) Find the equation of the tangent line to the curve the point (1, 1). y²(2 – x) = x³ at

A: Given curve is : y2(2-x) = x3

Q: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 7) Find an equation of the line tangent to the curve y = x+5 at x = 3. х-1

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Q: 2 at the point ( 2, 1 Find an equation of the tangent line to the graph of y = e y =

A: we have to find the equation of the tangent line to the given function. We know that slope of the…

Q: 3. Find the equation of the tangent line to the curve x'y+y°x= 30 at point (1,3).

A: Solve the given problem.

Q: 4) Estimate the instantaneous rate of change of function f(x) = x + 5x' +2 at x = -3 b) Determine…

A: Given that fx=x4+5x3+2First, we will find the instantaneous rate of change of the functionat x=-3.

Q: 2. Find the equation of the tangent line for the function 2 f(x) = x2 + - 3 at a = -2

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Q: 5) Find an equation of the tangent line to the curve y = sin²(x) cos(x) at the point (,0).

A: Slope of tangent,m  = dy/dx Equation of tangent to curve at point (x,y) y -y1 = m (x -x1 )

Q: 4. Find the equation of the tangent line to g(x) 8 at x = 3 |x²–1

A: The function is given by gx = 8x2-13 To evaluate: The equation of the tangent line to the graph of…

Q: 6) Find an equation of the tangent line to the graph of f (x) = 4 ln z at the point (1, 0).

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Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

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

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Q: 13. Find the equation of the tangent line to the curve x'y' + 4.xy = 12y at the point (2,1).

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Q: on the chain rule find the tangent line to graph y=(x+2/x+1)^2, at x=0

A: We have to find tangent line to y , first we will find  value of y at x=0.

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

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Q: 6. Find an equation of the tangent line to y = f(x) : = tan¬(2x) at x = 7

A: Given,

Q: Find the equation of tangent and vertical line to the curve g=x+1/x at point (0,1)

A: First we want to check whether the given point is in the domain of the given function.

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

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Q: 8. Find the equation of the horizontal tangent line to the curve y = -x + yx.

A: For horizontal  tangent line put the derivative  of function equals to zero

Q: 4. Find the equation of the tangent line to the curve f (x) = (x² – 4)(2x + 1) at x : -2.

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Q: 1 Find an equation of the line tangent to y at point (0, -). X-3

A: Given y=1x-3 at point 0,-13 To find equation of line tangent:

Q: 2. Find the equation of the tangent line to y at x = -5.

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Q: 2) Find the equation of the tangent line in slope intercept form to the curve x² + 4xy + y2 = 13 at…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 − x2 −…

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Q: curve at the following point:  y = 2/ 1 + e-x, (0,1)

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Q: Find an equation of the tangent line to the curve at the given point. y = 4.9x – x², (3,5.7) - y =…

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Q: 11. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? %3D a. -5 b. -6…

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Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

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Q: 1. Find the equation of the tangent line to x² – 3xy + y² = -1 at (2,1).

A: given that x2-3xy+y2=-1slope of tangent (m)= dydxdifferntiate the given curve with respect to…

Q: 1. find an equation of the line tangent to y = x-3 at point (O,-) %3D

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Q: 3 Find the equation of the tangent line to the curve x*y – xy = –2 at the point (-1, –1

A: Given: x4y-xy3=-2 and the points are (-1,-1)

Q: 9. Using first principles, determine the equation of the tangent line at point (2,2) on the curve…

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Q: 5. Find the equation of the tangent line (slope-intercept form) to the 5 at the point (6,1). x-1…

A: To determine the equation of the tangent line.

Q: 6. Find the equation of the tangent line to the curve 2x3 + xy + y° = 4 at the point (1, 1).

A: Firstly we can find slope .i.e, dydx at (1,1). Then slope intercept form  y-y1=m(x-x1)

Q: Find the equation of the tangent line to the curve at the given point. y = 3x − 2x^1/2   (1, 1)

A: