For the curve y = 5x – 2x3, if x .6 increases at the rate of 2 units/s, then find the rate of change of the * .slope of the curve when x = 3

Q: Solve for the Slope and Rate of Change of the following. 1. What is the slope of the graph y = -x2…

A: As per bartleby guidelines we are supposed to answer only 3 subparts per question. This post has 4…

Q: The deflection y (in m) of a 5.00-m beam as a function of the distance (in m) from one end is y =…

A: Topic : differentiation

Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x² units, (40 s xs 60) where x is the…

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Q: For the function y = x2 , find the instantaneous rate ofchange of y with respect to x when x = 3.

A: The instantaneous rate of change of y with respect to x is given by dy/dx

Q: For what point on the curve of y=5x^2+9x is the slope of a tangent line equal to -21?

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Q: Choose whether the following statement is true or false. The approximation of an instantaneous rate…

A: The given statement is:  The approximation of an instantaneous rate of change can be obtained by…

Q: If the demand for q units of a product priced at $p per unit is described by the equation 300 2g + 2…

A: Answer and explanation is given below

Q: For the function y=x2,compute the average rate of change between x=9 and x=10

A: We have to find the average rate of change of function.

Q: The area of a square with side s is A(s) s². What is the = rate of change of the area of a square…

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Q: Estimate the slope (in y-units per x-unit) of the tangent line to the curve. What is your estimate…

A: The slope of a graph represents the rate of change of the output with respect to the change in…

Q: 4x+2 find average rate of change from x=-1 t x=1

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Q: The curve for which y'' = 6 has a slope of –3 at its point of inflection (2, 3). Find the value of y…

A: y''' = 6 Implies, y" = 6x + a, where, a is a constant. &, y' = 3x² + ax + b, where, b is a…

Q: For the function y= 9x^2+8x+4,at the point x=4, find the following (A) the slope of the tangent to…

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Q: S(2) = 32+-4 ant line to f(2) (ak.a, the average rate of change of ) from input val

A: Please refer to the image below

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: For the function y = 4x2: (a) Find the average rate of change of y with respect to a over the…

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Q: The table shows a linear relationship between x and y. What is the rate of change of y with respect…

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Q: For what point on the curve of y = 3x - 6x is the slope of a tangent line equal to 0? %3D

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Q: Differentiate implicitly to find the slope of the curve at the given point. x2+y2 = 1; (4, 7) O 7…

A: The given equation is:x2+y2=1The point is 4, 7

Q: 1. What is the instantaneous slope of y = 5 at x = 5?

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Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

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: The relationship between food expenditure of 25 households (y) and their total expenditures (x) is…

A: Given: ln Y^=2.24+0.364 ln Xr2=0.886

Q: 2x+1 Aliza says that there is no tangent line with a negative slope for the f(x)% = Stella disagre…

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Q: The slope of the line through the distinct points (x1, yı) and (x2, Y2) can be interpreted as the…

A: To Determine: the slope of the line through the distinct points can be interpreted as the rate of…

Q: differentiate the functions and find the slope ofthe tangent line at the given value of the…

A: s'(t)=9·3t2-8·2t=27t2-16t

Q: What is the instantaneous slope of y == at z = 5?

A: for the instantaneous  slope for a function f(x) at x=a we have to find f'(x) and then put x=a in…

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

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Q: 8. What is the rate of change of the slope of the tangent line to the curve y =x – 3x2 +1 when x =…

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

A: First we will differentiate the given equation with respect to t using the chain rule of…

Q: Find the rate of change of y with respect to x when x=3000 and y=100

A: Given data:   The given expression of the function is 180x0.75y0.25=230,734. The given value of…

Q: consider the equation f(x) =5x2 find the average rate of change between x=3 and x=3+x

A: Given: the equation f(x) =5x2 and find the average rate of change between x =3 and x =3+ x

Q: Find the slope of the curve y^3+3x^2y-9y=-5 at the point (1,-1) and also find the rate of change…

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Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units, (40 < x< 60) where x is the…

A:

Q: Differentiate implicitly to find the slope of the curve at the given point. 3-y3=D5; (3,5) %3D 0 2…

A: We have to find the slope of the curve at the given point. For this we will find derivative dydx…

Q: currently 49 workers, find the instantaneous rate of change of monthly output with respect to the…

A: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units,    (40 ≤ x ≤ 60)  , where x…

Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

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Q: find the equation of slope of tangent and the equation of slope of normal for y = -2x* + 5x° 4 2 3…

A: Given that y=-2x4+5x2-3 Take the derivative, y'=-8x3+10x The equation of the slope is,…

Q: Find the rate of change of x with respect to p. 900 – x p = 0 < x< 900 бх

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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: Find the values of a and b if the tangent to y = ar² + bx at (1,5) has a slope of 8.

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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: Let ​h(x)=x^2−8x.   ​(a) Find the average rate of change from 4 to 7. ​(b) Find an equation of the…

A: Average rate change and secan line problem....

Q: The slope of the line through the distinct points (x1, y1) and (x2, y2) can be interpreted as the…

A: The slope of the line through the distinct points (x1, y1) and (x2, y2) is defined as…

Q: (1-x)2 13. For the curve y find the rate of change of slope at (2, ½)-

A: For the curve, y=1-x2x, to find the rate of change of slope at 2, 12.

Q: The instantaneous rate of change for the function Y=x^2+2x,  at x= 3

A: The rate of change of any function is given by dydx  at any point x=x0 ,that is derivative of 'y'…

Exponential Growth Model

The relation that represents an exponential function is: