The position of an object moving along a line is given by the function s(t)=-9t^2+27t Find the average velocity of the object over [1,7]

Q: Find the equation of the tangent and normal line of the function f(x) = 2x – 1 at the point (5, 3).

A: fx=2x-1   First find equation of tangent line of given function  We need to find the slope of…

Q: y = vx² – 9

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Q: find the slope of the line tangent to the curve x2=y2+3/2xy at (4,2)

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Q: Find the slope of the line tangent to the graph of f(x) = xe* at x = 0. %3D

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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: Find the slope of the line tangent to the curve x - 3xy + 4x = 2 at x = 1. -5/3 O 2/3 O 1/3 O 4/3

A: The given curve is: x3-3xy+4x=2 We need to find the slope of the line tangent to the given curve.…

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: 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 point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

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

A:

Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: Find the equation of the tangent line at x=9 for f(x) =X^3/2

A: I am attaching image so that you understand each and every step.

Q: Determine the slope of the line tangent to y = x+1 at x = 1 3x2

A: y = (x+1)/3x2 slope = dy/dx dy/dx = (3x2(1) - 6x(x+1))/9x4 slope at x=1 dy/dx = (3 - 6(2))/9 dy/dx =…

Q: Find the equation of tangent lineto the cubic x^3-6x^2+10x+8 parallel to the line y=x

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Q: .The line y + 2x = 0 is tangent to y = F(x). Determine F(x) if F(x) = 4x³ + 2.

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(z) = 7x² +…

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Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: Explanation: Given that,  y=2x3-3x2-10x+1     Concept Used: 1. Slope of the tangent is the first…

Q: If f(x) describes the position of an object over time, what is the average velocity on the interval…

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Q: Find an equation of the tangent to the curve f(x) = /x+ 7 that has slope %3D 4

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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: 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: What is the gradient of the tangent line to the curve y = 2x³ – 3x2 at the point with a = 2? |…

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Q: Find the slope of the tangent line on the curve y = x3 - 2x2 – x at x = -2. -6 O -19 O 19 O 6

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Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: Find the point where the tangent line to y = x² at x 0.7 crosses the x-axis.

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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: 2. Find the slope of the tangent to the curve y = 3 + 4x² - 2x³ at the point where x = a

A: given,y=3+4x2-2x3

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: The slope of the tangent to y = 2 – x2 at the point (1,1) is

A:

Q: Find the slope of the line tangent to the graph of x2+2xy2+3y=31 at th epoint (2, -3)

A: To determine the slope of the tangent at the point (2, -3).

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² − 2x³ at the point where x = a -

A: The equation of the curve is given by y = 3+4x2-2x3 To evaluate: The slope of the tangent to the…

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: the side of a sqaure is 10 cm. find the approximately, by using differential, the increase in the…

A: Given that side of a square a is 10cm and it is increased by 0.02cm.

Q: Find the x-coordinate of the point/s on the curve y = 2x – 3x² – 12x + 20 where the tangent line is…

A: The slope of the tangent line to the curve at point P(x,y) is given by,…

Q: 3. Find the slope of the line tangent to f(x) = In(4x² – 3) at (1,1).

A:

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: Find the slope of the tangent line to the curve −2x^2+xy+2y^3=−8 at the point (−3,2)

A: NOTE: Refresh your page if you can't see any equations. .

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

A: Given:

Q: Find the slope of the line tangent to the curve x^3 - 3xy + 4x = 2 at x=1.

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(z) = 6x² +…

A: Derivative is the rate of change of function with respect to the variable at some given point. Limit…

Q: Find the equation tangent line at a=2 for f(x)=2x²-3x+1 O y=15x-7 O None of these O y=5x+7 O y=5x-7

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Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

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Q: Find the point where the tangent line to y = 5x at x = 0.5 crosses the x-axis.

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Q: Find the equation of the tangent line to the curve f(x) = x³ln (x + 1) at the point (0, 0).

A: The given curve is: f(x)=x3 ln(x+1)

Q: Use the limit definition of the derivative to find the instantaneous rate of change c f(x) = 4x + 7x…

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x

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

A: equation of tangent line

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

A: The function f(x)=x2+2x-34. We have to find all x-values where the function f(x) has a horizontal…

Exponential Growth Model

The relation that represents an exponential function is: