If f(x) = 3x3 - 18 for 0 ≤ x ≤4
(a) Find any local maxima, minima or points of inflexion.
(b) Sketch the function, clearly marking and labeling thee domain and range and the global maximum and minimum.
(a) to find the maxima and minima, if they exist, we must find the critical points. we find these by setting f ' (x) = 0
then we can test them using the second derivative test, if you want. you can also use the first derivative test
to find POSSIBLE points of inflection, set f '' (x) = 0. and use the first derivative test on both sides of the points you find to see if the derivative keeps its sign (in which case, you have an inflection).
as far as (b) is concerned. $\displaystyle 3x^3$ looks pretty much like $\displaystyle x^3$ when you're sketching. the -18 says you shift the graph 18 units down. be sure to find the new x- and y-intercepts