Suppose f(x)=x2−2x million dollars are​ earned, where x is the number of years after 2000.   a. What is ​f(30​)? b. The answer to part​ (a) gives the number of millions of dollars earned for what​ year?

Q: Suppose f(x)=(x−1)/(x+6). Write an expression in terms of x and h that represents the average rate…

A: fx=x-1x+6

Q: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 300-cc organ at a rate of 5…

A: Given: the concentration of the drug carried by  the liquid=0.1g/cc liquid enters and leaves the…

Q: The amount of plutonium remaining from 1 kilogram after x years is given by the function…

A:

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=3f(x)+1x. If the…

A: Derivative of a function using the formula f′(x)=3f(x)+1x and f(3)=6. We know that approximate…

Q: The degree of the derivative of f(x) = (3–x)'(x – 12)° is

A:

Q: A body at a temperature of 0° F is placed in a room whose temperature is kept at 100°F. If after 10…

A:

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=5f(x)+3x. If the…

A:

Q: Suppose f(x)=(x−3)/(x+4) Write an expression in terms of x and h that represents the average rate of…

A: fx=x-3x+4 The average rate of change of f over any interval x, x+h is fx+h-fxh.

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Given that , The radioactive material is known to decay at a rate proportional to the amount…

Q: Find the second derivative of h(x) = x2 + 3x3. Simplify your answer, %3D

A:

Q: What is the first derivative of q(x) = In (4x² + 3x + 2)?

A:

Q: For what values is the function f(x)= ln(x+1)/x^2+1 continous? Can you please explain how to…

A: If , g(x) is continuous and h(x) is continuous. Then g(x) / h(x) is continuous.where h(x) not equal…

Q: Find the derivative of the function. h(x) = (4/x^2)+(6/x^3)

A:

Q: Which of the following functions grow faster than x2 as x→∞?Which grow at the same rate as x2? Which…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: If the total revenue function for a blender is R(x) = 41x – 0.01x² where x is the number of units…

A: Given that, the revenue R (in dollars) for a blender is given by  R(x) = 41x - 0.01x2 where x is the…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Let us assume that the rate of change of the amount of material is proportional to the amount of…

Q: Find the second derivative of the function h. h(x) = (10 – x2) (5x + 17)

A: Here, h(x)=(10-x2)(5x+17)

Q: What is the derivative of p(x)=(2x^4+2)^x

A: Using logarithmic differentiation we can find the derivative of the given function.

Q: Suppose f(x)=(x−4)/(x+4). Write an expression in terms of x and h that represents the average rate…

A: Given: fx=x-4x+4, To find: The expression of average rate of change of f over any interval x,x+h.

Q: There is a relationship between perceived corruption and human development in a country that can be…

A: Given data: The expression for the human development index is H(x)=0.3+0.28lnx (a) Given value of x…

Q: Find the second derivative of the function.

A: Given: f(x)=x2+3xx-4 To find f''

Q: certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: We will solve the radioactive decay problem.

Q: Where does the derivative of g(x)=(x^2)/((x^2)+3) = 0 or is undefined?

A: Given function, gx=x2x2+3

Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

A: We have to find the function whose tangent line has the slope 3x2+1 for each value of x and whose…

Q: The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be…

A:

Q: The number of daily users for Japan’s Line messaging service (in millions) can be approximated by…

A: The approximating function that represents the given scenario is: g(x)=53.1+63.1 ln(x) where x…

Q: Suppose f(x)=6x2+9x−12. Write an expression in terms of x and h that represents the average rate of…

A: The average rate of change is given by: f(x+h)-f(x)h

Q: If the total revenue function for a blender is R(x) = 28x – 0.01x² where x is the number of units…

A: To find The average rate of change of revenue R(x) as x increases from 10 to 20 units.

Q: If the total revenue function for a blender is R(x) = 52x − 0.01x2 where x is the number of units…

A: We have the total revenue function R(x) = 52x − 0.01x2.

Q: Find the second derivative of the function. f(x) = (3x° + 6)*

A:

Q: The usual estimate that each human-year corresponds to 7 dog-years is not very accurate for young…

A: Given: Accurate formula for converting human-years x into dog-years is, 10.5x if 0≤x≤221+4x-2 if…

Q: On the basis of data for the years 1911 through 1991, the expected life span of people in a country…

A: First find the number of years x from 1908 to date of birth of the person 1966 than put that x in…

Q: 33. Solve for the second-order derivative of the function below. Y = x 3x3 За

A: Differentiate two times wrt x

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

A: In a particular very small region, the consumer price index, C, depends on the current value of…

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rọa“, in millirems per hour.…

A:

Q: #12) Find the derivative of the function f(x) = 35x2-1

A: The solution of the problem is given in the next step.

Q: On the basis of data for the years 1911 through 1994, the expected life span of people in a country…

A: f(x) = 12.469 lnx +17.128x is the number of years from 1906 to person's birth year.expexted life…

Q: The usual estimate that each human-year corresponds to 7 dog-years is not very accurate for young…

A:

Q: 7. If h(x)=|2x- 3, what is the value of the derivative at x = -2?

A: According to the problem we have

Q: What is the relative error in estimating the first derivative of f (x) = 25x3-6x2 +7x - 88 at x-2,…

A:

Q: Evaluate the second derivative of the function at the given point f(x)=9/√x+9    (0,3)

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: In mathematics, two varying quantities are said to be in a relation of proportionality,…

Q: Find the second derivative of the function. f(x) = 8(2 − 2x)4 f"(x)=

A: Given,

Q: There is a relationship between perceived corruption and human development in a country that can be…

A: Given  H(x)=0.3+0.28 In x                 where H(x) is Human development index…

Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

A:

Q: Which of the following functions grow faster than x2 as x→ ∞?Which grow at the same rate as x2?…

A: Let f(x) and g(x) are two functions. 1) If limx→∞fxgx=∞ then f(x) grows faster than g(x) as x→∞. 2)…

Q: Find the requested value of the second derivative of the function. f(x)=4x4-8x2+5; find f"(0)

A: The given function is Now, taking first derivative of the given function