Thread: maxima, minima, points of inflexion

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.

Take the 1st derivative and set it to 0 to find maxima and minima

Also don't forget to try your endpoints to find local maxima and minima

Take the 2nd derivative and set it 0 to find the points of inflection

Originally Posted by brumby_3

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. looks pretty much like when you're sketching. the -18 says you shift the graph 18 units down. be sure to find the new x- and y-intercepts

Thanks I always forget to say "if they exist"