Exam 2: Functions, Limits and the Derivative

Find the constants m in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2. __________ Find the constants b in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2. __________

Find function f such that and

Let f be the function defined by Find and

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Find given that and .

At a temperature of , the volume V (in liters) of 1.33 g of is related to its pressure p (in atmospheres) by the formula . What is the average rate of change of V with respect to p as p increases from to ? What is the rate of change of V with respect to p when

For the supply equation where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 4 units of the commodity available in the market.

Find the values of x for which the function is continuous.

Let f be the function defined by f (x) = 3x + 9. Find and

Use the vertical-line test to determine whether the graph represents y as a function of x.Answer yes or no.

Use the method of bisection to find the root of the equation , accurate to two decimal places if necessary. __________

Use the intermediate value theorem to find the value of c such that . __________

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the function Find the rate of population growth at min.

Find the limit, if it exists.

Find and simplify for the function.

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

Find the limit, if it exists.

The ratio of working-age population to the elderly in the United States (including projections after 2000) is given by with t = 0 corresponding to the beginning of 1995.What will be the ratio at the beginning of 2005?

Find the functions f + g, f - g, fg, and

Find the limit.