Question

how to get the local extrema and points of inflection without a calculator

Answer 1

@freckles

Answer 2

@freckles

Answer 3

you will need to calculate f' and the critical numbers
and use first derivative test for local extrema
sometimes you can use second derivative test (there is only sometimes when it is inconclusive)

--

to find the POSSIBLE inflection points you solve f''=0 and may need to find when f'' does not exist but within the domain of the original function f
to find if the point it is really an inflection point you will have to look at the concavity on both sides of this so called possible inflection point

Answer 4

okay this is similar to what my txb is explaning it says if it's on an open interval f(c) is min

Answer 5

but I like ur explanation about inflection point! thanks again for ur help!