Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = -3x + 10. What are f(2) and f '(2) ? f(2) f '(2) -3 If g(x) =[f(x)]² , find the linear approximation for g(x) at a = 2. L(x) = | 16 + 8(x – 2)

Q: 4. Find the equation of the tangent line to the graph of f(x)= 2x² – In Vx at x = 1.

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Q: Apply the Chain Rule to find the tangent line to f(x) = 4/2x – 6e²-*at x = 2

A: The given problem is to find the tangent line to the given function at given point x=2 Given…

Q: 3 Find the slope of the tangent line to x/y +yVx = 10 at (1,8).

A: given: x3y + y3x= 10differentiate given equation with respect to xx3 ddxy + y ddx x3+ y3ddxx+ x ddx…

Q: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

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

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 7. If the tangent line to y = f(x) at (-1,3) passes through the point (2,1), find fl-1) and f'(-1).

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Q: 6. Find the equation of the tangent line to x² + 3xy + y² = 5 at the point (1, –4).

A: Given x2+3xy+y2=5       (1,-4)

Q: What is the first derivative of q(x) = In (4x² + 3x+2)? Select the correct answer below: In (8z + 3)…

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Q: Find the equation of the tangent line to the curve f(x) = - -x4 at x = 1. O T(x) = 1 + (-4)(x - 1) O…

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Q: 4. Find the equation of the tangent line to the graph of g(x) = v2-x at x =-7 %3D

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Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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Q: 4. Find the equation of the tangent line to the function y= In(x* -2) when x=3.

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Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

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Q: ) Find the equation of the tangent line ETL for f(x) = x³ - 2x +1 at x = −1

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Q: Where on the interval [0, 4] does ƒ(x) = 4x - x2 have a horizontal tangent line?

A: Determine the value for derivative of f(x) i.e f'(x). fx=4x−x2f'x=ddx4x−x2=ddx4x−ddxx2=4×ddxx−2xSo,…

Q: Compute the first derivative of y = 2x^4 - 6x^3 - 12x - 8 at the point x=0 based on the value at xo…

A: Five point FD Approximation and CD Approximation:--- ..  I this Error is 0%

Q: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15x3-0.2x2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: The equation of the tangent line to the graph of f(x) = vx+1 At the indicated point (3,2) is:…

A: The given function is fx=x+1. Evaluate the slope of the function at the point (3, 2) as follows.…

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: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: 15 - What is the approximate derivative of f(x) = 5x° + 4x? if we use forward difference method,…

A: Derivative of function at any point gives the slope of tangent to the function at that point.…

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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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: Find an equation of the tangent line to ln(2x-y+1) + cos(xy-2)=1 at the point (1,2)

A: Given:

Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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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: 3. Find the equation for the normal line (perpendicular to the tangent line) to f(x) = 2x3 – 2x at x…

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Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: Find the equation of the tangent line to y = 2r5 - 3x³ at the point where x = 0.7, with coefficients…

A: Methods to find the equation of the tangent at a point helps to find the required answer to the…

Q: 2. What is the equation of the tangent line to the curve y = x? - 2x +1 at point (3,4)? а. у3 2x — 2…

A: The equation of line is y-y1=mx-x1, where m is the slope of the curve.

Q: .2 Find the tangent line to y = x-x+2 at x=2.

A: Given - A function To find- Equation of tangent

Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

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Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

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Q: Find the slope of the tangent line to the given curve at the indicated point by using the two-step…

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Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: Find the equation of the tangent line to the graph of f(x)= x ln(2x+3) at the point (-1,0).

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Q: Find the equation of the tangent line (in point-slope form) to . 2 f(x) = 3 – 2x' + In(5x + e) at x…

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Q: Determine the equation of the tangent line to f(x) = ln(x-2) at x=4.

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Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: 2/ Find the equation of the tangent line at (0,0) to fex) = xex хе 2 -X

A: Given f(x)=xe-x2y=xe-x2Differentiate…

Q: 2. Determine the second derivative of f (x)=xe* at x = -2 with a step-size of h=0.50 using Central…

A: Given f(x) = x2e2x

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

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Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: 3. Find the equation of the tangent line to f(x) = 2x · sin (x) at the point (5, ).

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Q: 4. Find the equation of the tangent line to the function y = In (x² – 2) when x=3.

A: Question is solved.

Q: 4) Determine the equation of the tangent line to y=3x -5x² +10 at x= 1

A: The given equation is; y = 3x4 - 5x2 + 10  at x = 1