1. Consider the following function: f(x) = 3 + 6x + 5x2 + 3x3 + 4x4 Locate the minimum by finding the root of the derivative of this function. a. Newton's method xo = -1 (at least 5 iterations)

Q: 1. Find derivative of given function defined as follows. 7-29-22 y = (8x²-3x³) ³

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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: 7. Find the equation of the tangent line to the graph of the function 4xy + 5 In y = 28 at the point…

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Q: 8. Find all points on the graph of y = (x + 3)² at which the tangent line is parallel to the line…

A: The given graph is y = (x +3)2 To find the points on the graph at which tangent is parallel to the…

Q: 21. Find an equation of the tangent line to the graph of f(x) = x² - 2x at (a) (–2, 8); (b) (1, –1);…

A: fx=x2-2x

Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: 4. Determine the point(s) at which the graph of f (x) = has a horizontal tangent. Simplify as much…

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Q: 7. Find the equation of the tangent line (in the form y = mr+b) for the function f(x) = In(x-3)+6V…

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Q: 5. If f(x)= 5x² + 2x+1 is an invertible function, find the slope of the tangent line to f^(x) at the…

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Q: Suppose f(3) = 6 and f '(3) = 7. Find an equation of the tangent line to H(x) at x=3. %3D H(x) =…

A: We have,  Hx=x4-7fx, f3=6 and f'3=7 Using the chain rule of differentiation, H'x=x4-7·f'x+fx·4x3…

Q: Given the function g(x) = 8x – 84x? + 240x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: 22. Find an equation of the tangent line to the graph of f(x) = 4 - x² at (a) (-1,3); (b) (0, 4);…

A: Given: f(x)=4-x2 To Find: the equation of the tangent line to the graph at a) (-1, 3) b) (0, 4)…

Q: 1) Find the equation of the line tangent to the graph of f(x) = (x² + 1)(x³ + 1) at the point where…

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Q: 10. (a) Find an equation for the line tangent to f(x) = x³ + 4x² at the point x = 1.

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Q: 1. Find the equation of the tangent line at the given point. f (x) = e3x-x², (3,1)

A: We have to find

Q: Find the equation of the tangent line to the graph of the function f(x) = v2x² + 1 at the point…

A: Given that: f(x)=2x2+1        at point (2, 3)

Q: x²Sin(x) y = In 2x + 1 9.

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Q: 11. Find the equation of the tangent line at (2, 1) given In y = 4y² – x³ +4

A: 11. The equation of the curve is given by lny = 4y2-x3+4 To evaluate : The equation of the tangent…

Q: 4. Find all points on the curve y = log (x³ – x) at which the tangent line is horizontal.

A: We will find all the points on the curve at which the tangent line is horizontal using calculus as…

Q: 6. Find the tangent line equations for the given functions at the given point(s): x2 + 3xy + y3 = 15…

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Q: Find an equation of the tangent line to the graph of the function at the given point.

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Q: 4 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph of…

A: We know that if m is slope and (x1,y1) is point on line the equation of line is given as-  (y - y1 )…

Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: 6. Determine the x-value(s) of the point(s) on the graph of f (x) = 3x³ – 11x – 2 where the tangent…

A: The function f(x)=3x3-11x-2 where the tangent line is parallel to the line 10x-2y-18=0

Q: 19 Find all x-values where the tangent line is horizontal for the function v(x) = x3 − 12x + 10

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Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

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Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

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Q: 1. Find the equation of the tangent line at the given point. f(x) = e3x-x², (3,1)

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Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = V3x – 5

A: since you have posted multiple question in this question which are not interlinked so i have solved…

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. [5.1] Determine the equation of a line tangent to the curve of x = 1. f(x) = 5e* +1 at 2. [5.1]…

A: A detailed solution is given below

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = v3x – 5

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Q: 1- Find the equation of the tangent to the curve y = 2 sinx+ cos2x at the point x =a. 2- Find the…

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Q: 6. Find the equation of the tangent line to f(x)= = tan (2x) at the point (n/8, 1).

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Q: 12) Find the equation of the line tangent to g(x) = (3x + 11)ex-4 at x = 4.

A: ddxuv=vddxu-uddxvv2

Q: 13) Find an equation of the tangent line to the 22 – 4 2a + 5 at the point (0, graph of y =

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Q: 1. Find an equation of the tangent line to the graph of the function at the given point. f(x) = Inx*…

A: We have to find out the equation of tangent line

Q: 1. Find an equation of the tangent line to the graph of y = In (x² – 3) + e²-* at the point (2, 1).

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Q: 1. Find the equation of the tangent line to the graph of f (x) = x²e-* at x = 1. %3D

A: The given function is: fx=x2e-x In order to find the slope of the given function, find the…

Q: 12. Find the equation of the tangent line to the given function at the point (0,1). f(x) = In(3xe¬x)

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Q: 12. Find the equation of the tangent line to f (x) = x³ at the point P(1,1).

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Q: Suppose f(5) = 2, f'(5) = 8, and g(x) = In [f(x)+4]. Find an %3D equation of the tangent line to…

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Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

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Q: Find the equation of the tangent line to f(x)=4x+x^−1/2+1 at the point (4,35/2)

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Q: Find an equation of the tangent line to the graph of f(x) = 2 + e1−x at the point (1, 3).

A: We have to find equation of tangent line to the graph of function fx=2+e1-x at the point 1, 3. We…

Q: 1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x –…

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Q: 13. Given the function f(x) = 4 + x? %3D Find the 8x + 2 equation of the tangent line to the curve 1…

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Q: Suppose the line y= 7x - 1 is tangent to the curve y= f(x) when x = -8. If Newton's method is used…

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Q: 1- Find the equation of the tangent to the curve y= 2 sin x+ cos2x at the point x = n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 1. Find the equation of the tangent line to f(x)= 4x2 - 5x+2 at (-1,11).

A: We can find the equation of tangent to the curve as below.