3. If f (t) = -t + 5t + 3, describes the distance that a ball has traveled in meters, what is the average rate of change of the ball between t = 1 sec and t = 2 sec?

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: If the instantaneous rate of change of f(x) at (8, −7) is 9, write the equation of the line tangent…

A: It's given that the instantaneous rate of change  of  f(x) at  (8,-7) is 9 . We have to find the…

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: If the instantaneous rate of change of f(x) at (5,-9) is 3, write the equation of the line tangent…

A: For equation of tangent, one have to use y-b=m(x-a)Where (a,b) is the point, m is the slope.

Q: 2. Informally explain that a function is considered differentiable, if small changes dx, to the…

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Q: 3. What is the slope of the tangent line to y = 4* at x = 0?

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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: 4.) The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x? + 10x + 5000.…

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Q: For f(x)=x5, the instantaneous rate of change is known to be 405 at x=-3. Find the equation of the…

A: y=fx=x5instantaneous have of change is known to be 405 ,or x = -3∴ y=f-3=-35=-243

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: For f(x)=x5​, the instantaneous rate of change is known to be 5 at x=−1. Find the equation of the…

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Q: If the instantaneous rate of change of f(x) at (3, -5) is 9, write the equation of the line tangent…

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Q: A car traveling south towards Sioux Falls at 160 km/hr is chasing a truck traveling east away from…

A: Given, A car traveling south towards Sioux Falls at 160 km/hr is chasing a truck traveling east away…

Q: 4. A. Use the tangent line to find a linear approximation to the function f (x) = Vx near x = 64.…

A:

Q: If the instantaneous rate of change of f(x) at (4, −9) is 8, write the equation of the line tangent…

A: From the given statement, the rate of change of f(x) at (4, –9) is 8.That is,  f′(x) = 8.

Q: 2. Find the equation of the line tangent to x* – 3xy+ y³ = 1 when x = 0.

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Q: If the instantaneous rate of change of fx) at (9, -6) is 2, write the equation of the line tangent…

A:

Q: Suppose x and y are functions of third variable t. In the equation x2+y²=45, what are the values of…

A: This question is related to application of derivatives.

Q: What is the average rate of change of f(x) = f(x) = – 7 from z = 2 to a = 10? 1/2

A: To find the average rate of change of f(x) from x=2 to x=10.

Q: For f(x)=x3​, the instantaneous rate of change is known to be 3 at x=−1. Find the equation of the…

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Q: 3. fox =V X at X T6

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Q: What is the rate of change of y with respect to x for this function?

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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: Suppose y varies at a constant rate of change of 4 with respect to x (so that Δy=4⋅Δx ), and when…

A: topic - linear equation in two variables

Q: 14. Find the rate of change of y= (2x' +6x +4) at x =-1.

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Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

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Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: Slope of tangent line is ½. So the equation is of the form:

Q: If the instantaneous rate of change of f(x) at (4, −3) is 7, write the equation of the line tangent…

A: The objective is to find the equation of the tangent line to the graph of f(x) at x=4.

Q: If the demand for q units of a product priced at $p per unit is described by the equation 200 V29 +…

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Q: Fin the equation of the line tangent F(x) = xcos(x) + e^x at the point (0,2)

A:

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values dr of…

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Q: Suppose y = f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

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Q: Suppose a model for the surface area of a human body is given by S = 0.1094w0.425,0.725, where w is…

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Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 8. Use the difference quotient to find the approximate instantaneous rate of change for the function…

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Q: 6. Train E travels west toward Chicago station at 120 miles per hour while a second train N travels…

A: Train E =120 miles per hour  Train N=90 miles per hour

Q: What is the rate of change of y with respect to x for 9x-11y+2=0

A: Given that 9x-11y+2=0 We need to find the rate of change of y with respect to x that is dy/dx.

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.5x² –…

A:

Q: If the instantaneous rate of change of f(x) at (9, -7) is 6, write the equation of the line tangent…

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Q: For f(x)=x^3​, the instantaneous rate of change is known to be 27  at x=3. Find the equation of…

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Q: Suppose that f(x) = 3x² – 3. (A) Find the slope of the line tangent to f(x) at x = 5. (B) Find the…

A: We find f'(x) using the power rule Slope of the line tangent to f(x) at x=5 is given by f'(5) So to…

Q: Suppose x and y are functions of third variable t. In the equation +y=45, what are the values of the…

A:

Q: Suppose that f(x) = 5x² – 4. (A) Find the slope of the line tangent to f(x) at x = 5. (B Find the…

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Q: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

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Q: For the given curve y = 5x – 2x', when x increases at the rate of 2 units / sec, then how fast is…

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Q: If the instantaneous rate of change of f(x) at (6, −8) is 4, write the equation of the line tangent…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: If f(x) = 5x -3 , compute the instontoneus rate of change of Sx) at x-2. OA -3/49 O8.7/41 oc-7/41…

A: