I am having issues with this one problem,
Let be the function defined for less than or equal to less than or equal to by
(a) Find all values of for which
(b) Find the -coordinates of all minimum points of . Justify your answer.
(c) Find the -coordinates of all inflection points of . Justify your answer.
Thanks for all your help!
(A) can you find derivate of
use product rule to find second derivative
Now finish it
(C) for max and mim points, put f'(x) = 0 and find all x
then plug these values in f(x) to find all values of f(x) . FINISH IT
(B) out of the points find out the points where f(x) is minimum.
I am sorry for the late response.
so when i first differentiate i get which is the same as then when i differentiate again i get which equals 1 and when . how do i justify that without saying i looked at my gragh?
b)there is no minimum in the given interval of because when f'(x)=0 that point is a maximum on the original graph. correct?
c) infection points occur when so that is when and
are these correct?
sorry for be i meant to say that at and is a maximum on the original graph of . and yes, a point can not be a maximum and inflection. I know i did something wrong, but i can not figure it out.
is a point of inflection, that i know for sure but why is and not , i do not know. help please?
thank you so much, if i could click the thank you button more than once, i would. i have been trying so many different things. so the min is because that is the endpoint and in a closed interval you have to check the end points. i remember my teacher telling us this a loong time ago, i can't believe i forgot.
but for the points of inflection i am not sure i completely understand. the f''(x) graph i am looking at, it goes from positive y values to negative y values at and then it goes from negative y vlaues to positive y values at . isn't that a sign change?
so just checking again
b)there is a minimum at x= due to the endpoint test.