Find the first positive x value of x for which f(x)=sin(e^x) has an inflection point. Correctly take derivatives.
Hello, camjenson!
Your second derivative is incorrect.
Find the first positive value of for which has an inflection point.
We have: .
Then: .
Hence: .
And we must solve: .
Equation [1] has no solutions.
Equation [2] can be approximated.
Let
We have: .
And we can approximate a root of: .
Then back-substitute: .