For the function y = 6x² + 5x + 6, at the point x = 7, find the following. %3D (a) the slope of the tangent to the curve (b) the instantaneous rate of change of the function

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: Find the derivative. y = e(lnx)2

A: dydx=ddx e(lnx)2        =e(lnx)2 ddx2(ln x)         =e(lnx)2 2x

Q: With the given graph, estimate the instantaneous rate of change at x= -1 and show the steps. Next,…

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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…

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

Q: Find the instantaneous rate of change Of the function at the Speciried value of X flx)=X?-2; X -3

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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 demand x is the number of items that can be sold at a price of $p. For x p" implicitly 7p+600,…

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Q: Find the equation of the graph and estimate the instantaneous rate of change at x = 1

A: From graph we can conclude that the equation of this graph be a parabola i.e., a quadratic equation.…

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

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Q: For the given function, find the instantaneous rate of change at x= 4 Y=(x^2-2) (x^2 -6x +6)

A: For this problem, we have find derivate of given function at one time. And later substitute value of…

Q: find the rate of change. The reciprocal 1/x with respect to x when x = 1, 2, 3

A: The rate of change of a function is the value of the derivative of the function; thus, let the…

Q: Find the derivative of the function. y = log 4 V3x +2

A: The Answer is Option A

Q: Find the nth-order derivative of the function y=(3x2−2x)lnx, x>0.

A: Use the product rule

Q: If f(x) = 3x + 2x + 6, find the instantaneous rate of change of f(x) at x = 1. -

A: Topic - applications of derivativea Instantaneous Rate of change of f(x) at x is given by slope of…

Q: If f(x)=9x+6, find the instantaneous rate of change of f(x) at x=-5

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Q: Find the instantaneous rate of change for the function at the given value. f(x) =x+3x at x= - 1 The…

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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: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: In this we are going to use decay formula so I'm providing hand written solution for this

Q: 1. For function f (x) = 0.5*, state a) the average rate of change from x = -1 to x = 1 b) the…

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Q: 213 20 fet)= (9t+3)

A: The given function, f(t)=9t+323

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: Find the derivative of the function. y= log 4- x

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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: Find x0 given that the rate of change of y =2x2+x-1 with respect to x at x=x0 is 4

A: giveny =2x2+x-1 rate of change=4rate of change=dydxdydx=4x+1

Q: for the function f(x)= √2x+3, estimate the instantaneous rate of change at x=5. use h value of 0.01

A: The instantaneous rate of change of f at x = a is f'(a), if it exists,

Q: For the curve y = 5x – 2x3, if x .6 increases at the rate of 2 units/s, then find the rate of change…

A: We are given the curve: y=5x-2x3 Slope (m)=dydx=5-6x2 Rate of change of slope  = dmdt=0-12xdxdt Now…

Q: Find the rate of change of x with respect to p. 500 – X 0 < x < 500 8x

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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: Find the instantaneous rate of change for the function at the given value. f(x)=x + 2x at x= 0 The…

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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…

A: Given that the monthly output at the Olek Carpet Mill is

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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Q: determine the instantaneous rate of change at x = 2 for f(x) = 5x2 + 3x + 7

A: Topic :- Differentiation

Q: Find the instantaneous rate of change for each function at the given value: . ƒ(x) = x2 + 2x at x =…

A: we have to find the instantaneous rate of change of a given function   given function is ƒ(x) = x2…

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: Solved below

Q: The derivative of y=eSinh/x +cosh¬/x equals

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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: Find the instantaneous rate of change of g(x)=(x^3-sqrt(x))e^x+(x^5-2x+3)ln(x) when x=3. Round to…

A: The instantaneous rate of change of g(x) is:…

Q: For the functiony = (x2 + 2)(x3 − 4x),at(−2, 0)find the following.(a) the slope of the tangent…

A: y = (x2 + 2)(x3 − 4x) = x5 + 2x3 - 4x3 - 8x = x5 - 2x3 - 8x Recall famous law of differentiation:…

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: What is the instantaneous rate of change of A with respect to s when s is 4.00?

A: Given a square of area A in2 and length of the side s in To find the instantaneous rate of change of…

Q: The value of y varies at a constant rate of change of 1.7 with respect to x. If x varies from x=3 to…

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Q: a drug concentration curve is given by C(t)= 20te^-0.2t, which C in mg/ml and t in minutes. What is…

A: A drug cocentration curve isC(t)=20te-0.2tTo find the rate of concentration. We have to…

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

A: Given that the monthly output is Qx=15,000+2x2 units, where x is the number of workers. Find Q'52.

Q: If f(x) = 12x2 − x3, what is the rate of change of f '(x) at  (−1, 13)?

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Q: Find the instantaneous rate of change for the function at the given value f(x) =x +2x at x= 0 The…

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Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: Given the function g(x)=x² −2x³ +1, a. Estimate the instantaneous rate of change at x = 1. b. Will…

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Q: 7. If f (t) = -t2 + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

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Q: Given the function f(x) = x which of the following is a valid formula for the instantaneous rate of…

A: The given function fx=x23 The instantaneous rate of change is given by limh→0fa+h-fah

Exponential Growth Model

The relation that represents an exponential function is: