Questions from General Calculus

Q: (a). Find y' by implicit differentiation. (b

(a). Find y' by implicit differentiation. (b). Solve the equation explicitly for and differentiate to get y' in terms of x. (c). Check that your solutions to parts (a) and (b) are consistent by substi...

Q: The graph of the derivative f' of a function f is shown

The graph of the derivative f' of a function f is shown. (a). On what intervals is f increasing? Decreasing? (b). At what values of x does f have a local maximum? Local minimum? (c). If it is known...

Q: The graph of the derivative f' of a function f is shown

The graph of the derivative f' of a function f is shown. (a). On what intervals is f increasing? Decreasing? (b). At what values of x does f have a local maximum? Local minimum? (c). If it is known...

Q: Use the given graph of f to estimate the intervals on which

Use the given graph of f to estimate the intervals on which the derivative f' is increasing or decreasing.

Q: The graphs of a function f and its derivative f' are shown

The graphs of a function f and its derivative f' are shown. Which is bigger, f' (-1) or f"(1)?

Q: A graph of a population of yeast cells in a new laboratory

A graph of a population of yeast cells in a new laboratory culture as a function of time is shown. (a). Describe how the rate of population increase varies. (b). When is this rate highest? (c). On w...

Q: The table gives population densities for ring-necked pheasants (in

The table gives population densities for ring-necked pheasants (in number of pheasants per acre) on Pelee Island, Ontario. (a). Describe how the rate of change of population varies. (b). Estimate th...

Q: A particle is moving along a horizontal straight line. The graph

A particle is moving along a horizontal straight line. The graph of its position function (the distance to the right of a fixed point as a function of time) is shown. (a). When is the particle movin...

Q: Let K (t) be a measure of the knowledge you

Let K (t) be a measure of the knowledge you gain by studying for a test for t hours. Which do you think is larger, K (8) – K (7) or k (3) – K (2)? Is the graph of K concave upward or concave downward?...

Q: The graph of the derivative f' of a continuous function f is

The graph of the derivative f' of a continuous function f is shown. (a). On what intervals f is increasing? Decreasing? (b). At what values of x does f have a local maximum? Local minimum? (c). On w...