Find the maximum rate of change of fat the given point and the direction in which it occurs. f(x, у) %3 8y?/x, (2, 1) maximum rate of change direction

Q: 7x ar Find the rate of change of total profit, in dollars, with respect to time where R(x) dx C(x) =…

A: Given that: R(x)=7xC(x)=0.06x2+0.6x+80

Q: The atmospheric pressure at altitude h (kilometers) for 11 ≤ h ≤ 25 is approximately…

A: Given: P(h)=128e-0.157h

Q: approximate the acceleration

A: Given: Ruth rode recorded her velocity v(t), in miles per hour for the selected value of t, Over the…

Q: Q3/ The dimensions of a rectangular solid at a given instant (t.) are: L(t.)= 13 cm. W(t)-9 cm.…

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Q: Function f(x)=x2+5  Find the average rate of change between the points (x,f(x)) and (x+h,f(x+h))

A: GIven function:

Q: Water is discharged from a pipeline at a velocity v given by the function v = 1392 p 1/2 , where p…

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Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

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Q: (c) Find the direction(s) at which f(x, y) increase most rapidly and decrease most rapidly at the…

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Q: A particle moves along a straight line and has acceleration given by s" = 5t. Its initial velocityis…

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Q: Find the maximum rate of change of the function f(x, y) = 5y5 at the point (2,4) (Round the answer…

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Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

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Q: Find the rate of change of total​ revenue, cost, and profit with respect to time. Assume that​ R(x)…

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

A: The given question can be solved as shown in step2.

Q: For function f (x, y) y? x²+1 Find the maximum rate of change of f at the point (1, 2)

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Q: de Given that Q = find the rate of change of Q with respect to x. sec x %3D Va5+3'

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Q: For the graph y = f(x) = 3x² – x + 2 (i) (ii) Q3. %| - Find the average rate of change of y w.r.t x…

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Q: he maximum rate of change of f at the given point and the direction in which it occurs. f(x, v) =…

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Q: Cet f(x) =. 1 %3D (a) Find the slope of the tangent line to y = f(x) at ¤ = 2. Fad At what rate are…

A: Topic:- application of derivatives

Q: A square with side x cm, is changing with time where x(t) = 4t – 2. What is the rate of change of…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (a) Find the slope m of the tangent to the cûrve y = 7/Vx at the point where x = a > 0. m = (b) Find…

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Q: Find the average rate of change of g(z) = 4r'- 2 from z= - 2 to z = 4 %3D

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Q: 2. Given f (x) = ax² + b. a) Calculate the secant slope for xe[0, 2]. b) Find the rate of change at…

A: we have to calculate the following

Q: An airplane takes off from an airport at sea level and its altitude (in feet) at time t (in seconds)…

A: We have to find rate of climb of airplane at t=180 sec.

Q: What is the instantaneous rate of change of y=√√zat z=2? 0 ม O - O none of the above 0

A: The function is given by y = x To evaluate: The instantaneous rate of change of the function at x=2.

Q: The velocity of a particle moving along a line is given by v(t)=t^3−4t^2 meters per second. Find the…

A: To find the displacement of the particle, velocity should be integrated w.r.t. time.

Q: Consider a function y = 1 / x (a) Find the rate of change of the average of y with respect to x in…

A: Derivatives

Q: 1Find the average rate of change * the interval [-1,4] for the function over The function y = (x –…

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Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: Sketch the graph of y = v4-x², - 2<x<2. a

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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: Flnd the maximum rate of change of f (x.y) =e*²+e*+2y at P (2,1) 29 e4 V 29 e 16 O 7e4 O Viet

A: gradient of function fx, y=ex2+ex+2y, at 2, 1

Q: Find the maximum rate of change of f(s,t)= te^{st} at the point (0,5).

A: In this question we have to find the maximum rate of change.

Q: Consider a function y = 1 / x a) Find the rate of instantaneous change of y with respect to x at x…

A: a) y = 1 / x dy / dx = - 1 / x2

Q: Find the distance s covered by a point moving with linear velocity v for the given time t.   v = 21…

A: Consider the given velocity v=21mihr and t=20min

Q: The rate of flow of a continuous income stream (in thousands of dollars per day) is given by f(t) =…

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Q: The velocity function (in meters per second) is given by v(t) = t2 - 2t - 3, for a particle moving…

A: We will use formula for the Displacement and distance in terms of Velocity function

Q: 5. Let f(x, y) = x² - y² x² + y² a. In which direction should you move from the point (1,1) to…

A: Maximum rate of change occurs in the direction of gradient vector of the function.

Q: Consider the function y=x/x-1  , where the unit for x is hours and the unit for y is km. a)…

A: Use formula to calculate

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A: *to find:- rate of change of total revenue. rate of change of cost. rate of change of profit.…

Q: The tangent line to the graph of y = f(x) at the point (8, 9) has the equation y = 2x – 7. %3D (a)…

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Q: The normal to the curve y = e+3kx has gradient 5 when x = 0. Find the value of k. Select one: 1 25…

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Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: Consider an isosceles triangle of base 16 inches and edges z, and assume that z is a function of…

A: Base of triangle = 16in  Edges = z in

Q: Find the rate of change of a population of size P(t) = ť + 4t + 6 at time t = 3. %3D

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Q: Find the average rate of change of the function from t1 to t2.

A: Given the position function is st=-16t2+v0t+s0 and t1=0, t2=2 To find the average rate of change

Q: At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level.…

A: ft=2sin2t Now velocity is the derivative of position with respect to time. So differentiating…

Q: z = x2 + y2, where x and y are increasing at the constant rates of 2 units per second and 3 units…

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