Questions from General Calculus

Q: The function f (x) = √(x2 - 6x +

The function f (x) = √(x2 - 6x + 10) has one relative minimum point for x ≥ 0. Find it.

Q: Radium 226 is used in cancer radiotherapy. Let P(t

Radium 226 is used in cancer radiotherapy. Let P(t) be the number of grams of radium 226 in a sample remaining after t years, and let P(t) satisfy the differential equation P(t) = -.00043P(t), P(0) =...

Q: The length, x, of the edge of a cube is

The length, x, of the edge of a cube is increasing. (a) Write the chain rule for dV/dt, the time rate of change of the volume of the cube. (b) For what value of x is dV/dt equal to 12 times the rate o...

Q: Many relations in biology are expressed by power functions, known as

Many relations in biology are expressed by power functions, known as allometric equations, of the form y = kxa, where k and a are constants. For example, the weight of a male hognose snake is approxim...

Q: Suppose that P, y, and t are variables, where

Suppose that P, y, and t are variables, where P is a function of y and y is a function of t. (a) Write the derivative symbols for the following quantities: (i) the rate of change of y with respect to...

Q: Differentiate the function. y = 1 / (√x –

Differentiate the function. y = 1 / (√x – 2)

Q: Suppose that Q, x, and y are variables, where

Suppose that Q, x, and y are variables, where Q is a function of x and x is a function of y. (Read this carefully.) (a) Write the derivative symbols for the following quantities: (i) the rate of chang...

Q: When a company produces and sells x thousand units per week,

When a company produces and sells x thousand units per week, its total weekly profit is P thousand dollars, where P = 200x / (100 + x2). The production level at t weeks from the present is x = 4 + 2...

Q: The cost of manufacturing x cases of cereal is C dollars,

The cost of manufacturing x cases of cereal is C dollars, where C = 3x + 4√x + 2. Weekly production at t weeks from the present is estimated to be x = 6200 + 100t cases. (a) Find the marginal cost, dC...

Q: Ecologists estimate that, when the population of a certain city is

Ecologists estimate that, when the population of a certain city is x thousand persons, the average level L of carbon monoxide in the air above the city will be L ppm (parts per million), where L = 10...