For #1-2, find the derivative of the function
1985 AB6
The figure above shows the graph of [pic], the derivative of a function f. The domain of the function f is the set of all x such that [pic].
a) For what values of x, [pic], does f have a relative maximum? A relative minimum? Justify your answer.
b) For what values of x is the graph of f concave up? Justify your answer.
c) Use the information found in parts (a) and (b) and the fact that [pic]to sketch a possible graph of f on the axes provided below.
1991 AB5
Let f be a function that is even and continuous on the closed interval [-3, 3]. The function f and its derivatives have the properties indicated in the table below.
|x |0 |[pic] |1 |[pic] |2 |[pic] |
|[pic] |1 |Positive |0 |Negative |-1 |Negative |
|[pic] |Undefined |Negative |0 |Negative |Undefined |Positive |
|[pic] |Undefined |Positive |0 |Negative |Undefined |Negative |
a) Find the x-coordinate of each point at which f attains an absolute maximum value or an absolute minimum value. For each x-coordinate you give, state whether f attains an absolute maximum or an absolute minimum.
b) Find the x-coordinate of each point of inflection on the graph of f. Justify your answer.
c) Sketch the graph of a function with all the given characteristics of f.
1996 AB1
Note: This is the graph of the derivative of f, not the graph of f.
The figure above shows the graph of [pic], the derivative of a function f. The domain of f is the set of all real numbers x such that [pic].
a) For what values of x does f have a relative maximum? Why?
b) For what values of x does f have a relative minimum? Why?
c) On what intervals is the graph of f concave upward? Use [pic]to justify your answer.
d) Suppose that [pic]. Draw a sketch that shows the general shape of the graph of the function f on the open interval [pic].
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