Forthefunctionf(x)=2x3 -x+4,
a. At what point(s) would the graph of f(x) have horizontal tangent lines? (You may give the
coordinate(s) as decimals if you wish).
b. On what intervals is the graph of f(x) sloping upward? Sloping downward?
c. On what intervals is the graph of f(x) concave up? Concave down?

let f (x)=27x-x^3
a. find all the critical points of f.
b. find all the inflexible points of f.
c. on what interval(s) is f an increasing function? a decreasing function?
d. on what intervals is the graph of f concave up? concave down?

The graph of the first derivative of a function is shown. (Assume the function is defined only for .)

a. On what interval(s) is  increasing? 

b. At what value(s) of does  have a local maximum? At what value(s) of  does  have a local minimum? 

c. On what interval(s) is  concave upward? On what interval(s) is  concave downward? 

d. What are the -coordinate(s) of the inflection point of ?

Graphical Reasoning

The graph of the first derivative of a function f on the interval is shown. Use the graph to answer each question.

(a) On what interval(s) is f decreasing?

(b) On what interval(s) is the graph of f concave downward?

(c) At what x-value(s) does f have relative extrema?

(d) At what x-value(s) does the graph of f have a point of inflection?