Chapter 3, Problem 56RE

Differentiate the function

-2Fonslowcountyscho The average value of gold per ounce over time is modeled by V(†) = 45†+ 279, where t = time in years since 2000. According to this function, how many years will it take for the gold to be worth $639?

How do I determine the interval?

Let S = f(r) = 4pir^2 be a function whose input (r) is the radius of a sphere (in inches) and whose output (S) is the surface area of the sphere. a What is the domain of this function? b) Function f has the inverse. Explain why. c) Describe what f does, that is explain what the inputs and outputs are in the context of the question. d) Describe, in words the meaning of f-1(200) and evaluate the value. e) Explain what it means to solve the equation f (r) = 200? f) Compare the answers to d) and e). What's your conclusion? Write it by completing the sentence f-*(200) is such a number r, that = 200 g) Based on part f) write the general statement about an inverse f-'(question is fully continued and clear in the image attached)

Assume ?(?) is a differentiable function. Which of the following expressions is equal to∫ ?3?′(?) ⅆ?.a) ?^3?(?) − ∫ 3?^2?(?) ⅆ?b) ?^3?′′(?) − ∫ 3?^2?(?) ⅆ?c) ?^3?(?) − ∫1/4?^4?(?) ⅆ?d) None of the above

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Select the statement that is false about the difference quotient.   The difference quotient can be represented by f(x+h)−f(x)(x+h)−x or f(x+h)−f(x)h The difference quotient is a more general form of the average rate of change of a function on an interval h units long. The difference quotient describes the general behavior of a function over some interval h units long when the rate of change is not constant. As the value of h gets smaller and smaller, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)). As the value of h gets larger and larger, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)).

Describe the increasing, decreasing, and constant behwior of the function, (Enter your onswers uning interval notation, If an ansen does not euist, enter CNE) [ f(x)=x^{4} / 2 \] inctesing decremaing Constant Find the point where the behwvior of the function chang

To determine the weather, a meteorologist uses the function T = x^2y^3z, where T represents the temperature in degrees Celsius in terms of the position in meters. A probe is sent in a straight line, determined by the direction (−2, −1, 2) passing through the point (1, −2,1). What is the rate of the temperature change as the probe passes through the point? A) −9.333 °C/mB) 16.000 °C/mC) −32.000 °C/mD) 5.333 °C/m