3. If f (t) = -t² + 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: Suppose that a company can produce 12000 units when the number of hours of skilled labor y and…

A:

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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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: Find the slope of the tangent to the curve y x3 at (6, 3) xy + 6 dx (Enter undef if the slope is not…

A: Given that: y2=x3xy+6 at (6, 3)

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

A:

Q: 4. [ ]Find the derivative of y with respect to the given independent variable: Ins 7x (a) ex³y = 2x…

A: Given equation ex2y=2x+2y   As per our guideline, we  supposed to answer only the first three…

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: 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: In what directions is the derivative of ƒ(x, y) = (x2 - y2 )/ (x2 + y2 ) at P(1, 1) equal to zero?

A: Given, , the unit vector is , here directional derivative is given as,

Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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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…

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: What is b > 0 if the tangent line to y = bx at x = 0 has slope 2?

A: Our Aim is to find thr value of b given that the tangent line to y=bx-(i)at x=0 has slope 2.

Q: 3. Find the slope of the tangent at x = 1 for y = ln(2x + 3) a) 2 b) = d) In(5)

A: As per Bartleby guidelines rule I am answering only first question as both question are different…

Q: 5. Find the equation of the tangent line for: x = vt + 9, y= at (4,-)

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

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

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Q: 1) Find an equation to the line tangent to y = (x – 3) 2 at x = 0.

A:

Q: 4. Find the equation of a line tangent to f (x) = –x² – 4x at x = -1.

A:

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

A:

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

A: The given function is fx=x+1. Evaluate the slope of the function at the point (3, 2) as follows.…

Q: 3. For the fiunction g(x) = x - 2x² –1, at what tangent point(s) is the instantaneous rate of change…

A: given function :

Q: 5) Find an equation to the line tangent to y = (x +3)³ at x = -3.

A: as per bartleby guidelines  i can do only first question. please ask other question seperately.

Q: 4. Find the equation of the tangent line to g(x) 8 at x = 3 |x²–1

A: The function is given by gx = 8x2-13 To evaluate: The equation of the tangent line to the graph of…

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: Find the maximum rate of change of f at the given point and the direction in which it occur f(x, y)…

A: Topic- Vectro

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

A: Given,   x2+y2=45To find dydt, when dxdt=-2 and x=3

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: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: 4y4 at the Find the maximum rate of change of the function f(x, y) point (5,1)

A:

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

A:

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: Suppose that a company’s marginal revenue from the manufacture and sale of eggbeaters is dr/ dx = 2…

A: To determine the expected revenue from a production run.

Q: Suppose that a company’s marginal revenue from the manufacture and sale of eggbeaters is dr dx = 2 -…

A: To Determine:  How much money should the company expect from a production run of x = 3 thousand…

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: Find the slope of the tangent to the curve y2 ln(x) + x2y = 7 at (1, 7)

A:

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

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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: 9. Consider the interval [0, 2n] for the function y sec x. State an x- value at which the…

A: Given query is to find value of x for different conditions for instantaneous rate of change.

Q: 3. Find the slope of the tangent line to r²e♥ + y²e² = 2e at (1,1).

A: Please see the answer below

Q: 5) Find an equation to the line tangent to y= (x + 3)³ at x =-3.

A:

Q: 9) Find the equation of the tangent line to: y = (1+x) e*when x=0

A:

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

A:

Q: 4. Find the slope of the line tangent to the graph of the equation -ey +y° = 7+ 2x at the point…

A: Given query is to find the slope of the tangent at given point.

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

A: equation of tangent line

Q: 4) Determine the equation of the tangent line to y=3x -5x² +10 at x= 1

A: The given equation is; y = 3x4 - 5x2 + 10  at x = 1