The position of an object moving along a line is given by the function s(t) = - 9t +54t. Find the average velocity of the object over the following intervals. (a) [1, 5] (c) [1, 3] (b) [1, 4] (d) [1, 1+ h] where h>0 is any real number.

Q: Find the equation of the tangent line to the function f(x) = x3 + a2 – x – 3 at the point where x…

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Q: 7. Find the slope of the tangent line to the graph at (1,1): x²y² – 9x² – 4y² = 0 %3D r-9r-4y = 0…

A: find the slope of the tangent line to the graph at 1,1; x2y2-9x2-4y2=0 differentiate the equation…

Q: Find the derivative using the following information.

A: Equation of tangent to curve g(x) at x=2 is y=-3x+2. Its slope is m=-3. Since slope of tangent to…

Q: Find h'(-2) if h = f • g, f(x) = -6x2 – 4 and the equation of the tangent line of g at -2 is y = -9x…

A: Slope of y=-9x+6 is = -9 This line is tangent to g at x=-2  So we get: g'(-2)= -9   The tangent line…

Q: Find an equation for the line tangent to the graph of f at (2,15), where f is given by…

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Q: ) Find the equation of the tangent line to f(x)= (36+2x2)-1/2 at x=0  y= (b) Use your answer to…

A: We use the fact that f(X) is approximately equals to f(a)+ f'(a)(x-a), which is tangent to line to…

Q: For which value(s) of x does f(x)=−x^3/3−2x^2+3x−8 have a tangent line of slope 7?

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Q: Let f(x) = 6x + 2 tangent line to the graph of f(x) at the point (0, – 3) is given by y = mx + b for…

A: The objective is to find the equation of the tangent line.

Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: The equation of the tangent line to f(x) = 5x2 + 7 at x = 0 is a y = 5x + 7 b y = 7 y = 2x + 14 O d…

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Q: 4. At what point on the graph of y =x2 is the tangent line parallel to the line 2x – 4y = 3?

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

A: By using the derivative and slope intercept form required tangent equation is :

Q: Find an equation of the tangent line to the graph of f (z) = -2² + 3z – 2 at the point (2, 0)

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Q: Find all the points on the curve x² y² + 2xy = 3 where the slope of the tangent is -1. O (1,1) O…

A: We have find possible point where the slope of the tangent is -1

Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

Q: Find the equation of the tangent line to f-l x+4 at the point P (,0) for f(x) = 3x + 3

A: f(x)=(x+4)(3x+3)=x+13(x+1)+33(x+1)=13+1x+1 f'(x)=-1(x+1)2 f''(x)=2(x+1)3 the slope of the tangent at…

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 an equation of the tangent to the curve f(x) = /x + 8 that has slope 4 %3D - OA. 1 y =7x-3 O…

A: Equation of the line in slope-point form is:        m = slope (x1, y1) = point on the line

Q: Find the slope of the line tangent to the given curve at the indicated point. a. f (x) = 3x + 10 at…

A: Given function,f(x)=3x+10,Aim:- To find the slope of the tangent of the curve f(x) at (-3,1)Let…

Q: Find an equation of the line tangent to the graph of the function: f(x) = V2x² – 1 at point P(-1;1).

A: Given:- f(x) = (2x2-1)(1/3)  To find:- Equation of tangent line at point p(-1, 1) on given curve

Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

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: A particle moves along the x-axis so that at time t\ge 0t≥0 its velocity is given by…

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Q: Given: f(x)=x2+2 find the equation of a line tangent at point P(1,3) using limits

A: To find the equation of a line tangent at point P(1,3) on below curve using limits.

Q: Find the equation of the tangent line to the curve x2 + 4y2 = 8 and parallel to the line x+2y=8.

A: Given curve is x2+4y2=8. To find equation of tangent line to the given curve which is parallel to…

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: Determine the value of a, given that the line ax+y+1 = 0 is tangent to the graph of y= ax-6x+1 at x…

A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: Find the equation of the line tangent to y = 3x² + x +1 at x = -3 Oy=-17x - 26 Oy=6x-3 Oy=-17x - 3…

A: Given that y=3x2+x+1, x=3 We know that the equation of the tangent is y-y1=mx-x1 where m is the…

Q: Find h'(-1) if h = fog, f(x) 3x2 8 and the equation of the tangent line of g at --1 is y = -2x +7.

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Q: 3. Find the equation of the tangent to y = 1-x² 3x+7 at the point where x = 1.

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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: 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: Find f(4) and f' (4), assuming that the tangent line to y = f(x) at a = 4 is y = -6x + 2. %3D

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Q: 2 at x 3 3x The equation of the line tangent to f(x) = 2 is |

A:

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: Find h'(-2) if h= fog. f(z) = 372 + 8 and the equation of the tangent line of g at-2 is y= 4x 6.

A: Here we have to find h'(-2) if h=f∘g , g(x) =3x2+8 and the equation of the tangent line of g at -2…

Q: Find an equation of the line tangent to the level curve of the function x 3xy passing through the…

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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: Find all points (x, y) on the graph of f(x) = x° - 5x + 26x + 19 with tangent lines parallel to the…

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Q: Find the equation of a line tangent to the given functions at the given points of tangency. 1) f(x)…

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Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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Q: Find the equation of the line tangent to f(x)=3/(2x+1)at the point (1, f(1))

A: Given function is  fx=32x+1

Q: Find the slope of the line tangent to the curve y =x-2x+ 1 at x 1 01 O 1/2 O 1/3 O 1/4

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Q: 3. Find the equation of the tangent line to the graph of x²y + 9xy= 162 at the point (-3, 6).

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Q: Find an equation of the line tangent to f(x) = Va at (4, 2).

A: equation of tangent line