Given the function , x is contained in the set (0,1)
A) Find the coordinates of any points where the graph of f has a horizontal tangent line.
B) Find the coordinates of any points of inflection on graph f
C) Find lim as AND lim as
D) Sketch graph of f using info obtained in a,b,c, with coordinates, max, min, etc.
The first 2 parts are based on units I did a WHILE ago ...
Do I do this for A?
(because 0 = horizontal line)
And solve for x?
Part a, my math solver on the calculator says -1.7632 (I had to use the absolute value of x to put in for the natural log).
But I'm confused here since x is supposed to be contained in the set from 0 to 1.
VonNemo19, thanks for the help, I'll look into that in more depth once I understand part a and b more.
Ahh, I get it.
So how does everything look?
Part A
x = 0.6065
y = -0.184 (Makes sense? - plugged it back in f(x))
Answer: (0.607, -0.184)
Part B
(Plugged back in f ' (x) )
Answer: (0.223, -0.446)
Part C
Answer: Zero (For Both)
Part D is just graphing, I should be fine with that.
^yes, I used L'Hopital's rule, but didn't show it there (takes a while for me to type the latex). It came out to be -2x.
The only weird thing is, when I graph this on my calc, the point of inflection for part b doesn't make sense since the y value is -0.446 in part b but the graph on my calc is more like -0.2.
What is the purpose of doing that? I'm just wondering since it seems like I still get lim f '(X) = 0.
Also, I understand that e=^(-3/2) but I'm confused about the y value for the point of inflection. My calculator shows that the lowest point of the graph of f(x) is -0.183 so why does the point of inflection I have in part b have y=-0.446?