Find the exact length of the curve f (x) = 1+ 6x7 on the interval 0 < x <1. Use a complete sentence, including units and write the solution in exact form. Do not use a decimal approximation. Show all of your work.

Q: Find all points on the graph of f(x) = x +a where the tangent line is parallel to the line y = 28x.…

A: Consider the function f(x) = x3 + x Slope of the tangent to f(x) is the derivative of f(x). f'(x) =…

Q: Find an equation of the line L tangent to the graph of f(x) = 8x +1 at x = 1/2.

A: Calculate the y-coordinate of the point where the tangent has to be drawn. Substitute 12 for x in…

Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

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Q: f(x)

A: We will find the equation of tangent.

Q: Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7)

A: We will find out the required equation of tangent.

Q: 4. Find the point on the curve y = 2x² – 12x + 5 where the tangent is horizontal.

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Q: Determine the slope of the tangent line to the curve (;² – 2x – 8) 2 -9 R(x) = at the point where…

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Q: Find the length of the curve y x² Inx 8 at (2 <x< 4)? -

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Q: x-1 f(x) = x= 1 at (2₁²) x+1

A: The objective of the question is determine the slope of the line tangent.

Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: Find the exact length of the curve on the given interval. Show at least 3 steps to justify your…

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Q: Find equation of the tan gent line to the curve f(x) = /16–4x at (3,2) a)

A: To Determine: a. Find the equation tangent line to the curve

Q: Find the tangent line of the function f(x) = - 4Vx at x = 4, and the point at which tangent %3D line…

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Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

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Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

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Q: At which point on the curve y = -2 + 2et – 3x is the tangent line parallel to the line 3x – y = 5?…

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Q: 4. Find the slope of the line tangent to the graph of 1 f (x) = 2x4 – 32x3 + 17x2 – 9x + 4 at x 2 -…

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Q: Find all values of x such that the tangent line to the graph of y = 5x² – 16x + 5 is steeper than…

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Q: The shortest distance from the point (5, 10) to the curve x2 = 12y is: 5.127 6.445 4.331 3.474

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Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is parallel to the…

A: Given: y = 2x3-3x2-12x+20 Tangent line is parallel to x - axis. To find: The points on the given…

Q: Find the equation of the tangent f (x) = 4x – 8vx at x = 16.

A: Find the equation of tangent of fx=4x-8x at x=16.   Substitute x=16 into fx=4x-8x to find the…

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

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

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Q: Find the equation of the tangent line to f(x) = 8x² – 5x – 40 at (3,17). %3D

A: Solution of the problem as follows

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

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Q: Find all points on the curve y = x³ + 2x² - 6x + 5 where the tangent is parallel to the line 2x + y…

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Q: Find all x-values where f(x) = (x² + 2x – 3)4 has a horizontal tangent line.

A: We find f ' (x) using the chain rule and the power rule. f(x)=(x2+2x-3)4…

Q: Find the equation of the tangent line to f(x) = x^2 −3x+5 at the point x = 3.

A: Given function , fx= x2-3x+5 at the point x=3 ,at x=3 , f3= 32-3x3+5             f3=9-9+5=5Hence ,…

Q: find equation of both the tangent lines to the elipse x^2+4y^2=36 that pass through the point(12,3)

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Q: Find an equation of the tangent line to the graph of  y = x(x + 2)4 at the point (2, 512).

A: The tangent is given by dydx So, In this question we differentiate y with respect to x and then put…

Q: Find an equation for the line tangent to the graph of f at (2, 28), where f is given by f(x) = 5x³ –…

A: Given function is fx=5x3-5x2+8. To find an equation of tangent line to the graph at point 2,28.…

Q: Find the length of the curve x2 1 In(1 – x) 2 4 1 between x = 0 and x 2

A: Recall: Length of the curve y=f(x) is given by on the interval a,b is…

Q: The slope of the tangent line to f(x) = 3x² – 1 at x = 2 is 12. true false

A: The solution of the problem is given in the next step.

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

A: Given : fx = -3x3 -2x2 -1

Q: What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=O?

A:

Q: Find the equation of the tangent line to the function f(x)=x3+3x2+x+4 at the point where x=−2. Give…

A: we have to find tangent line at x=-2given

Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1given

Q: Find the length of the curve : y = + from x = 1 to x = 3 - 3 4x

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Q: Write an equation of the tangent line to the curve f(x) = answer in the form Ar+By+C =0. 3x at the…

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Q: Find the equation of the tangent line to f(x) = (36 + 4x²)¯ at x = Use your answer to (a) to…

A: (a) Given,              f(x)=(36+4x2)-12       at  x=0.

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 the exact length of the curve. X=1/3sqrt(y)(y-3), 9 less than or equal to Y less than or equal…

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

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Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: At what point on the parabola y=3x^2+2x is the tangent line parallel to the line y=10x-2? Use first…

A: We have to find the point.

Q: Find the exact length of the curve over the given interval. 2sxs3 4x'

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Q: 1 Find the length of the curve ソ= 9 from x =1 to x=2. 28x7,

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