Originally Posted by
williamb Given f(x) = e^(-5x) sin(1x) , 0< x < pi/2
a) Find the second derivative
b) suppose that f has a point of inflection at x=c. Using the result of a), you can formulate the equation for c in the form:
tan 1c = K
where K is some constant.
Find the constant K as well as the points of inflection
C) Find the (open) intervals of concavity. If there is more than one interval enter using the union symbol U. Enter the empty set as {}
"f is concave upward on open intervals _________"
"f is concave downward on open intervals _________"
Alright so i found the second derivative:
f''(x) = e^(-5x) * (24sinx - 10cosx)
and in order for there to be inflection points where x = c, f''(c) = 0
I also know that for finding concavity(part c) i need to test points, which i can do on my own once i figure out part b!
I'm stuck on isolating "c" , i know this seems like grade 2 stuff by now, but still.
here's where i'm at ..
0 = e^(-5x) * (24sinx - 10cosx)
0 = ln[e^(-5x)] * (24sinx - 10cosx)
0 = (-5x) ln(e) * (24sinx - 10cosx)
we replace x with c..
0 = (-5c) ln(e) * (24sinc- 10cosc)
but i get so lost here. How do i isolate??! obviously i'm missing something/have done something wrong.
thanks for your help
Britt