Find a function f such that f'(x) = r and the line 4r - y = 3 is tangent to the graph of f.

Q: Estimate the slope of the tangent line of the function f(x) = 2e* at the point x = e. %3=

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Q: Determine the equation of the tangent line to f(x)=xx-1 at x=1. y=x y=x+1 x=1 y=1

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Q: Find the exact slope of the tangent line to sin (x) y = f(x) = 2x + S at the point where x = 2

A: we have the function y=f(x)=2x+sin(x)2 we have to find slope at point x=π6

Q: Find the Equation of tangent line of the function f(x) = 1 + csc(x) – /cos(x) 2n 4+V3 23 At the…

A: Consider the provided function, fx=1+cscx-cosx and the given point 2π3,4+323. Find the equation of…

Q: Find the derivative of f(x, y) = xey + cosxy at the point (2,0) in the ection.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Find the equation of the tangent line to y = = at x = 1. y - V2 = - V7 (x - 1) A) E (x - 1) -- x y -…

A: The solution is given as

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: Find the equation of the tangent line to the curve when x has the given value. f(x) = -,; x = 3 X-2…

A: Given that fx=7x-2 Evaluate fx=7x-2 at x = 3.     fx=73-2f(x)=7 That is y1=7 Find the derivative:…

Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: Find the derivative of y with respect to x. y = tan 9x-1- csc3x, x > %3D dy dx

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Q: Determine the point on f(x)= 2x^e where the tangent is parallel to the line y= 2x-12

A: The equation of the curve is  f(x) = 2xe The line parallel to the tangent line on the graph of the…

Q: Find the equation of the tangent line to the graph of y = f(x) at r = 3. %3D f(x) = In(x – 6|) y =

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Q: Find the equation of the tangent line. to y=f(x) at point P. %3D

A: We have to find the equation of tangent to y=f(x) at P.

Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

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Q: Pls help ASAP

A: This question is related to equation of straight line, we will use differentiation to find the…

Q: Determine the derivative of the function defined by h(x,y) = Arctan (2) + V3Arcsin () at the point…

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Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Find the equation of tangent line to the curve f(x) = 2 – dt 1+t at the point x = 1.

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Q: Find an equation of the tangent line to f(x) = x° – 2x +1 at the point (0, 1).

A: The given function is: f(x)=x3-2x+1

Q: Find the equation of the tangent line to the curve f( x) = Assume f'( x) =- and x = 1.

A: Answer and explanation is given below....

Q: Find the point of intersection of the tangent line to y=sin 2x) at y=0 and the line x+2y=5-

A: Given: y=sin(2x)  and y=0       substituting y=0 in y=sin(2x)then    0=sin(2x)         2x=0…

Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: Find the derivative of the funciton F(x) = dt. F'(x) =

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Q: Find the equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

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Q: The slope of the tangent line to f(x) = cos(x) · sin(x) at x - 2т is

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Q: Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1, 1) in the direction…

A: We have to find the derivative of the function fx,y=2x2-y2 at the point M=1,1 in the direction…

Q: Find the slope of the line tangent to f(x) = tan x at x=-. 4

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Q: Find the equation of the tangent line to the curve y = Vx – 3 at the point (4, 1). - o y = }x - 3 2…

A: Explanation of the answer is as follows

Q: Find the equation of the tangent line to the curvef (x) = -x' + 2x at x = 1. о Тx) 3D 1 + (-1)(х —…

A: To find the equation of tangent line to the curve at x=1

Q: Find the equation of the tangent line on the curve defined by 2xy- y² =1 at x = 1. A y=x-1 B y=1 ©…

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Q: |Find the point(s) on the curve f(x) = x² where the tangent is parallel to the line 4x-y-1= (

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Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

Q: Compute the derivative of f (x) = (x – 3r) cos(r). -

A: You will find the derivative of the given function using the product rule of differentiation which…

Q: Find the equation for the tangent line to the curve y=f(x) at the give x-value. f(x)=ex^2-1 at x=1

A: equation of the tangent at the point ( x1,y1) with slope  y - y1 = slope ( x - x1)

Q: Find the equation of the tangent line on the curve f(x) = V5x + 6 at x = 2.

A: Proceed as shown below...

Q: The equation of the tangent line of f(x) 3 e* at x = 0 is %3D y

A: We have to find the equation of the tangent line of the given function at the given point   The…

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: Determine the equation of the tangent line to f(x) = sin(x) at x = π/3

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Q: Find the equation of the tangent line to the curve f(x)= Va. Assume f'( x) 1 at x = 4.

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Q: ) Find the equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

A: Given:

Q: Find the derivative of F(x)

A: To Determine: find the derivative of F(x) Given: we have Fx=∫2x3costdt Explanation: we have a…

Q: Find the point on the curve y = x³ + x2 – 1 where the tangent is perpendicular to the line y = -x

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Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx <2n?…

A: We get the slope y' of the tangent to the function y=tan x-x by differentiating it with respect to…

Q: The slope of the tangent line to the graph of xy = In(x² + y²) at the point (1, 0) is

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: -2 In(x) Consider the function f(x, y) = 3y

A: We have to find the derivative of the function f(x,y) in the direction u=-5,2.…

Q: Find the equation of the tangent line to f(x)=-2sin(x) at x=0

A: We have to find the equation of tangent line

Q: Find the gradient of the tangent line to the curve x² + y =10 at x=1, where y > 0. %3D

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