Find the value of the constant k that makes the function continuous. 2x - 2x - 12 if x 3 g(x) = X- 3 kx-8 if x 3 k%=

Q: A coffee shop finds that at the price of $3.00, demand for their popular cappuccino drink is 3000…

A: Given that: At price of $3.00, demand = 3000 cups a year.For every $0.25 decrease in price, demand…

Q: Find the value of the constant k that makes the function continuous.

A: A function is relation between set of inputs and output. The piece-wise function is a function which…

Q: Determine the smallest value of the constant a for which the graph of the function f(x) = a^x−x is…

A: Since f(x) should always be greater than x axis ⇒f(x)>0ax-x>0ax>xTake log both…

Q: The function f(x) = 4ᴫx3/3 describes the volume, f(x), of a sphere of radius x inches. If the radius…

A: f(x) = 4πx33 Volume of sphere , f(x) = 4πx33 where,  x is the radius of sphere in inches.…

Q: Find maximum revenue for the revenue function R((x) = 377x - 0.9x-. (Round your answer to the…

A: From the given data R(x)=377x - 0.9x2 To find the maximum revenue dRxdx=0 377-0.9(2x)=0 377-1.8x=0…

Q: A producer of door frame chin-up bars has determined that the revenue from the production and sale…

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Q: Consider the following. = -0.1s3 + 6s² + 400 Find the amount s of advertising (in thousands of…

A: The point of diminishing returns refers to the inflection point of a return function or the maximum…

Q: The rate of population change in a town is given as 1000 (7 + 0.2t) ^ ((- 3) / 2). If the town's…

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Q: Which of the following graphs or equations have an average rate of change of 2 from the x-values 0…

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Q: Find the critical values of the function below. **x-24x? 8 -x³–24x² f(x)

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Q: Find the intervals of increase and decrease for the given function. t f (t) = (t+ 3)2

A: Given,      f(t)=t(t+3)2

Q: For a particular financial methodology, the risk-reward function was defined as y=x(Inx-2), where y…

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Q: If n is positive and even, where is the graph of f(x) = xn increasing and where is it decreasing?

A: For f(x)= xn  where n is positive and even. for these type of function the general graph is given…

Q: h(x)= 4/5 x5 +3x4 -7x3 -15/2 x2 +20x+1 local max & local min?

A: Given that To find local max and local min

Q: Find the rate of change between O and 1 y Save 20 16 12 8- f 4- ++X -4 -3 -2 -1 1 2 3 4 -4 -8+ -12…

A: Consider the given figure. We have to find the rate of change between 0 to 1. Let us take two point…

Q: d) Find the value of the constants ' a’ and b ’ that makes the function continuous at x= 3 ах + b ;…

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: Consider the given function,First find the derivative of the given function,

Q: Consider the following. P = -0.1s3 + 6s2 + 400 Find the amount s of advertising (in thousands of…

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Q: f (x) = 2x² – 3x + 2 Find the instantaneous rate of change at x = 2

A: The instantaneous rate of change of a function is given by the first derivative of the function. The…

Q: What values of a and b maximize the value of ! (7x-x) dx? a

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Q: In 2003 the number of online viewers was projected to grow according to the function. N(t)= 52t0.531…

A: As t=1 corresponds to 2003 then the value of t corresponds to 2010 is 2010-2003+1=8 Put this t=8…

Q: A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of…

A: Given,           A company has found that its expenditure rate per day in hundreds of dollars on a…

Q: Suppose that the function y = f(x) is decreasing on the interval [ - 2, 7].(a) Over what interval is…

A: Given: Suppose that the function y = f(x) is decreasing on the interval [ - 2, 7].

Q: For a particular financial methodology, the risk-reward function was defined as y=x(Inx-2), where y…

A: The risk-reward function,    y=xlnx-2y=units of reward, x=units of risk

Q: Consider the following. P = -0.1s3 + 6s² + 400 Find the amount s of advertising (in thousands of…

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Q: Find P(x), the profit function.

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Q: Which function shows a positive rate of change? x -2 -1| 0| 1 y 13 9 51 1 2 3 y -4 -6 -8 - 10 O f(x)…

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Q: f(x)%= V36-x² .2

A: In which interval f(x)=36-x2 is increasing and decreasing?

Q: State the interval(s) over which the function is (a) increasing (b) decreasing (c) constant

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Q: f(x) = is the range in which the function is decreasing.

A: fx=exx Differentiating with respect to x, we get f'x=dexdx·x-dxdx·exx2…

Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

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Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

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Q: By 2019, nearly $1 out of every $5 spent in the U.S. economy is projected to go for health care. The…

A: The figure is:

Q: Find the relative maxima and relative minima, if a does not exist, enter DNE.) f(x) = 3x - 10x³ + 10…

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Q: For some positive constant , a patient's temperature change, T , due to a dose, D , of a drug is…

A: Given: For some positive constant c and D=Drug Dose  T=Patient's temperature change T=C2-D3D2

Q: The interval in which the given function is decreasing is at 3 points y = x3 – x2 – 5x - 4 (-00, -1)…

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Q: Find the point of diminishing returns for the revenue function R(x)=-2/3(x^3-12x^2-6), 0 less than…

A: The given  revenue function is Rx=-23x3-12x2-6. in the interval 0≤x≤8. Since a point of diminishing…

Q: In the theory of learning, the rate at which a subject is memorised is assumed to be proportional to…

A: The subject to be memorized is given by At at time t. The total amount of subject to be memorized is…

Q: Find the intervals of increase and decrease  for the function.   f(x)= ln(lnx-4)

A: Simple increasing and decreasing problem.....

Q: f(x)=9x^2+180x+1 Relative maxima: Relative minima:

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Q: If g(x) = 3x + 6x2 + 4. What is the value of the instantaneous rate of change of g(x) when x = -1?…

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Q: Give the increasing and decreasing intervals and relative extrema    f(x)=e^(-2x^2+x)

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Q: Find the maximum profit and the number of units x that must be produced and sold in order to yield…

A: Given: The revenue function is Rx=x2+110x+60. The cost function is Cx=1.1x2+10x+80.   Determine the…

Q: The sales function for a product is given by S(x)=127+30.6x2−0.6x3S(x)=127+30.6x2−0.6x3, where x…

A: Given Sales function for a product is, S(x)=127+30.6x2-0.6x3,  where x represents thousands of…

Q: 2. f(x) = 6x - 1 slope: of f = of g y-intercept: of f= of g=

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Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: The demand for a particular item is given by the function D(x)=1500-3X^2. find the consumers surplus…

A: Given equilibrium price = 300 and demand function.

Q: P(x) = -400x + 6,800x – 12,000 dollars. At what rate is profit changing with respect to the level of…

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Q: Given the function g(x) = -x2 – 3x +5, determine the average rate of change of the function over the…

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Q: Use the formula below to find the instantaneous rate of change of the function at the given x-value.…

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