How do you sketch the curve #y=e^x-sinx# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?
Identify those critical points from the first and second derivatives of the function. Then you can "sketch" the curve knowing the basic shape.
The first derivative will identify inflection points. The second derivative will show their direction. Intercepts are "solutions = where
See the following reference for details in calculation and interpretation:
Weisstein, Eric W. "First Derivative Test." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FirstDerivativeTest.html
Weisstein, Eric W. "Second Derivative Test." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SecondDerivativeTest.html